
Class X-fe^5r 



Book 



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PRKSi:XTI-:i) BY 



The D. Van No^rand Company ' 

intend this book to be sold to the Public 
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or reduction. 



ELECTRIC TRAINS 



ELECTRIC TRAINS 



H. M^ HOBART, M.Inst.C.E. 



AUTHOR OF 



AND " DYNAMO DESIGN 



88 ILLUSTRATIONS 




D. VAN NOSTRAND COMPANY 

23 MURRAY AND 27 WARREN STREETS 

NEW YORK 

1910 






6^'' 
^^\^^ 



'Gifi 
Sidney B. s-i \\\ 




^^ 



I 

/ 



Vi 



\o 



PREFACE 

It is iadicative of the rapid progress of the application of electricity 
to the propulsion of railway trains, that it is no longer possible, 
within the bounds of a single volume, to cover the entire subject 
with any approach to adequacy. Indeed, in limiting my programme 
to Electric Trains, I have still found the field too wide to be dealt 
with effectively, and I have consequently confined the treatment to 
Electric Trains for City and Suburban Service, thus purposely 
excluding the large and important subject of Electric Locomotives. 
Even with this restricted programme I have considered that it is 
impossible, without incurring the risk of diverting the reader's atten- 
tion from the logical development of my subject, to introduce much 
material descriptive of the apparatus coinprised in the electrical 
equipment. I have endeavoured to make amends for this by 
including references to publications in which useful descriptive matter 
may be found. 

There is a dearth of published matter where a reader can find set 
forth coherent and simple descriptions of thoroughly practical methods 
of calculating the required energy for operating electric railways. I 
do not know of any work other than the present book in which 
the approximate estimation of the cost of the rolling stock of 
electrically-propelled motor-coaches and trains, proportioned for a 
given service, is worked out rationally and with the certainty of 
arriving at reliable results for the comparative purposes of pre- 
liminary estimates. Most of the interesting and valuable essays in 
these directions are too ponderous, and their authors have been 
hampered by the involved and cumbersome methods which they have 
employed. Although portions of these essays are of great value to 
those interested in electric railways, they are usually seriously 
overweighted with digressions of none too relevant a nature, and the 
methods set forth are needlessly complex. 



vi PREFACE 

The problems involved in railway electrification work are, in 
their broad aspects, not amenable to useful solution by other than 
more or less empirical methods based on rough, practical tests. 
After the broad solution has been reached, and after the main features 
of the scheme have been laid down, theriy and then only, is the stage 
reached when close detailed work on the many component points 
involved should be undertaken. 

The electrical engineer will be out of his element in designing 
trucks and car bodies, and he will be well advised, even in the 
matter of the suitable location of the electrical apparatus, to confine 
his part to that of simply placing at the disposal of experienced 
steam-railway engineers his special knowledge of electrical apparatus 
and methods. Holding this belief, I have not included in this 
treatise matters relating to details of the design of trucks and car 
bodies. I consider that it would be inappropriate, at any rate in a 
book of the small compass of the present treatise, to include 
information on these points. 

I am hopeful that not only electrical engineers and students, but 
also railway engineers, will find the present treatise of assistance 
in making clear the most pertinent considerations governing the 
electrical aspects of the design and operation of Electric Trains for 
City and Suburban Service, and with a view to the achievement of 
this purpose, I have not considered it expedient to apply the space 
at my disposal to other than the most distinctly relevant portions of 
the subject. 

I have taken the mile as the unit of length. It is, however, 
characteristic of electrical engineering, that calculations are expe- 
dited by the use of the metric system. Consequently for short lengths 
I have employed the meter, of which there are 1609 in the mile. 
Accelerations are given in miles per hour per second, and I have 
employed the abbreviation " ml phps," since the abbreviation " m " 
is reserved for the meter. With the desire to avoid bigotry in this 
matter of units, I have, in such cases as the dimensions of rolling 
stock, freely employed feet and inches. The British ton and the metric 
ton differ from one another by only 1*8 per cent., and since this varia- 
tion is of absolutely no consequence in such a subject as that dealt 
with in the present treatise, I have regarded the British ton and the 
metric ton as identical. Engineers should keep in mind that in the 



PREFACE vii 

case of many descriptions of electric railway work carried out in 
America, the authors of the British papers and books republishing 
these descriptions have often not taken the trouble to translate the 
weights from the 2000-lb ton used in America to the British or metric 
ton used everywhere else. There are many instances in which it would 
appear that the authors of these papers have not noticed that another 
than the British ton is employed. In view of the complacency with 
which this 11 per cent, indefiniteness is assimilated by the engineer- 
ing community, I see no reason to anticipate criticism of my plan of 
ignoring the 1*8 per cent, difference between the British and metric 
ton, and I consider it a great advantage that in this matter of the 
ton, we have a unit common to both the British and the metric 
systems. It should not be difficult to take the next step, and to 
employ the one-thousandth part of the ton as the smaller unit of 
weight. Whether this be described as 0*001 ton or as 1 kg is 
immaterial. In this book I have employed the kilogram as a con- 
venient designation for the thousandth part of the ton. Tempera- 
tures are in all cases given in the Centigrade scale. 

In building up a basis for my methods, I have perused with 
much profit Aspinall's papers ("Proc, I.C.E.," vol. cxlvii. p. 241, 
and "Proc, I.M.E.," 1909, No. 2, p. 423), Carter's contributions 
("Journal, I.E.E.," vol. xxxvi. p. 231. Eugby Eng. Society, Feb. 
18, 1909), and papers by Armstrong, Potter, Hutchinson and others, 
published in various volumes of the " Transactions of the A.I.E.E." 
While the reader will find in the text numerous reference to descrip- 
tions of apparatus, I cannot refrain from specially calling attention 
to a treatise entitled "Electric Traction," by Wilson and Lydall, 
since with respect to this special feature of descriptions of apparatus, 
the book is, in my opinion, unexcelled. " Electric Eailway Engineer- 
ing," in which Mr. H. F. Parsha-ll and the present author collabo- 
rated, and Mr. Philip Dawson's " Electric Traction on Kailways," 
also contain a great deal of detailed information concerning many 
notable cases of electrically operated railways. The present treatise 
is not to be considered as an alternative of any of the above- 
mentioned books, but as an attempt to accomplish the specific task 
indicated in this preface. 

I wish to take this opportunity of expressing my thanks to 
Mr. J. E. Chapman, Chief Engineer of the Underground Electric 



viii PREFACE 

Railways Co., of London ; to Mr. R. P. Brousson, General Manager 
of the Great Northern and City Railway ; to Mr. J. A. F. Aspiaall, 
General Manager of the Lancashire and Yorkshire Railway ; to Mr. 
H. F. Parshall, Consulting Engineer to the Central London Railway ; 
to Mr. E. P. Grove, Chief Engineer of the Central London Railway ; 
to Mr. C. H. Merz, Consulting Engineer to the North Eastern 
Railway ; and to Messrs. Dick, Kerr and Co., and Messrs. The 
Siemens- Schuckert Dynamo Works, for their courtesies in providing 
me with data of their undertakings. 



CONTENTS 

CHAPTER PAQR 

Preface ............ v 

List of Tables xi 

List of Figures . xv 

List of Abbreviations employed ........ xix 

I. Speed-time Diagrams .......... 1 

II. The Influence of the Number of Stops per Mile, and of the Duration of Each 

Stop 19 

III. The Preponderating Influence of Momentum in a Service with Frequent 

Stops 27 

IV. A Method of estimating the Energy Consumption of Trains, on the 

Assumption of Negligible Train-friction and of 100 per cent. Efficiency 

of the Electrical Equipment on the Train ...... 44 

V. The Efficiency of the Electrical Equipment 67 

VI. The Determination of the Efficiency of the Electrical Equipment of the 

Trains on the Central London Railway ...... 87 

VII. Analysis of some Energy Consumption Tests of Trains on the Great Northern 

Piccadilly and Brompton Eailway ....... 97 

VIII. Acceleration and Tractive Force . . . . . . . .108 

IX. Train-friction 116 

X. The Predetermination of the Power-Curve for a Given Journey . . .132 
XI. The Heysham, Morecambe and Lancaster Electrified Section of the Midland 

Railway ........... 145 

XII. The Heating of Railway Motors 158 

XIII. The Weights and Costs of Electrical Equipments and of Electrically 

Equipped Trains . . . . . . . . . .166 

XIV. Summary and Conclusions ......... 181 

Index ............ 199 



LIST OF TABLES 



TABLE 

I. 

II. 

III. 

IV. 
V. 

VI. 

VII. 

VIII. 
IX. 

X. 

XI. 

XII. 

XIII. 



XIV 



XV. 
XVI. 

XVII. 



XVIII. 



XIX. 



Data obtained from the Curves of Figs. 1 to 3 

Conversion Table for Speed and Acceleration . . . . . 

Data obtained from the Speed-time Diagram of Fig. 8 . 

Data obtained from Figs. 9 and 11 ...... . 

Influence of Dm-ation of Stop on the Schedule Speed for an Average 
Speed of 22 ml ph, and for a Length of Eun of 0*5 mile . . . 

Influence of Duration of Stop on the Schedule Speed for an Average 
Speed of 22 ml ph, and for a Length of Eun of 1 mile 

Influence of Duration of Stop on the Schedule Speed for an Average 
Speed of 11 ml ph, and for a Length of Eun of 0'5 mile . 

Data obtained from the Speed-time Diagram of Fig. 18 ... 

Tractive Force required at Axles to overcome Train Resistance at Various 
Speeds ........... 

Energy required at Axles to overcome Train- friction at Various Speeds . 

Allocation of Power consumed by a Train during a Given Eun 

Allocation of Energy consumed by a Train during a Given Eun 

Showing the Duration of, and the Average Speed and Distance covered 
during, the Accelerating, Constant Speed and Decelerating Periods of 
the Speed-time Diagram of Fig. 26, when taken to represent a 1-mile 
Eun at Schedule Speed of 18 ml ph 

Showing the Duration of, and the Average Speed and Distance covered 
during, the Accelerating, Constant Speed and Decelerating Periods 
of a Eepresentative Speed-time Diagram similar to Fig. 26 

Values of C for Various Accelerations and Decelerations 

Calculation of the Energy Consumption of Trains for Assumed Frictionless 
Euns ........... 

Schedule Speeds attainable with Various Values of Energy Input, and 
with Different Lengths of Eun, assuming Frictionless Conditions and 
100 per cent. EflSciency of Electrical Equipment .... 

Energy Consumption for a 1*5 mile Eun with Various Values of Acceleration 
and Deceleration (assuming Frictionless Euns and Electrical Equipment 
of 100 per cent. Efficiency) ........ 

Limiting Values of Speed and Energy Consumption, neglecting Train- 
friction and assuming 100 per cent. Efficiency of Electrical Equipment, 
the Speed-time Diagrams having no Coasting Period (see Figs. 29 
and 32) ....... Folding Inset facing 



PAGE 

4 

7-8 

12 

16 

19 

20 

20 
28 

32 
33 
36 
37 



46 



47 
48 

50 



52 



55 



56 



Xll 



LIST OF TABLES 



TABLE 



PAGE 



58 



60 



61 
71 



XX. Energy Consumption for 1-mile Eun at Various Schedule Speeds, 
assuming no Train-friction and 100 per cent. Efficiency of the 
Electrical Equipment ........ 

XXI. Showing the Duration of, and the Average Speed and Distance 
covered during, the Accelerating, Constant Speed and Decelerat- 
ing Periods of the Speed-time Diagram / in Fig. 33 
XXII. Energy Consumption of Trains stopping Once per Mile and running at 
Diflferent Schedule Speeds, assuming no Train-friction and 100 
per cent. Efficiency ........ 

XXIII. Analysis of Train Tests on the Lancashire and Yorkshire Railway 

XXIV. Continued Analysis of Train Tests on the Lancashire and Yorkshire 

Railway .......... 71 

XXV. Over-all Efficiencies of Electrical Equipment for Various Schedule 

Speeds and Runs ......... 76 

XXVI. Estimates of the Energy Consumption and Amount of Equipment 
required by Trains operating to a Given Schedule under Normal 

Working Conditions 78-79 

XXVII. Specification of Four-coach Train on the Lancashire and Yorkshire 

Railway 84-86 

XXVIII. Analysis of Train Tests on the Central London Railway ... 91 

XXIX. Continued Analysis of Train Tests on the Central London Railway . 92 

XXX. Continued Analysis of Train Tests on the Central London Railway . 93 

XXXI. Specification of a Six-coach Train on the Central London Railway 94-95 

XXXII. Average Values observed during Two Train Tests on the Great 

Northern Piccadilly and Brompton Railway .... 100 

XXXIII. Analysis of Train Tests on the Great Northern Piccadilly and 

Brompton Railway . . . . . . . .101 

XXXIV. Specification of Six- and Four-coach Trains on the Great Northern 

Piccadilly and Brompton Railway ..... 102-104 

XXXV. Showing the Loading of the Great Northern Piccadilly and Brompton 

Railway Motors during the Tests A and B of Table XXXIII. 
XXXVI. Calculations of the Power-Curve for the Speed-time Diagram 
indicated in Fig. 61 ....... . 

XXXVII. Tractive Force required for the Propulsion at Constant Speed of a 

100-ton Train 

XXXVIIl. Showing the Influence on the Tractive Resistance of a Train, of adding 
Additional Trailer-coaches . . . . 

XXXIX. Values of Frictional Resistance deduced from Berlin-Zossen Tests with 
an 83-ton, 75 -foot Coach ....... 

XL. Showing the Influence of the Increased Efficiency of Electrical 
Equipment (with Increased Load) on the Frictional Resistance, as 
deduced from Readings of Electrical Instruments during Tests 
with an Assumed Constant Efficiency for all the Tests 
XLT. Average Values of the Results obtained during Tests of the Tractive 
Resistance on the Lancashire and Yorkshire Railway 
XLII. Values of the Frictional Resistance of Locomotives as determined from 
Tests by Hutchinson ........ 



106 



112 



117 



121 



122 



124 



126 



127 



LIST OF TABLES 



xui 



TABLE PAGE 

XLIir. Values of the Tractive Resistance of Trains of Various Weights, as 

obtained from Armstrong's Analysis of Tests by Davis . . 128 

XLIV, Arnold and Potter's Results of Tests for the Energy Consumption of 
Trains of Various Weights under Schedule Conditions (One Mile 

Run) 128 

XLV. Additional Tractive Effort required on Curves .... 130 

XLVI. Data of Gear Ratios of Several Typical Motors .... 134 

XLVII. Estimation of the Current Input to each Motor and to the Train during 

the Run indicated in Fig. 66 137 

XLVIII. Derivation of the Motor Speed-Curve ...... 143 

XLIX. Energy Consumption of Trains on the Electrified Section of the 

Midland Railway ......... 147 

L. Specification of Electric Trains on Midland Railway (Heysham, 

Morecambe and Lancaster Branch) ..... 150-152 

LI. Analysis of Tests on the Midland Electric Trains . . . .154 

LII. Values of Internal Losses in Motors at Rated Load . . . .159 

LIII. Calculations of C.L.R. Motor Losses in Service .... 160 

LIV. Calculations of G.N.P. & B.R. Motor Losses in Service . . . 162 
LV. Calculation of L. & Y. R. Motor Losses in Service .... 163 

LVI. Comparison of Motor Losses at Rated Load and during Service . . 163 

LVII. Comparison of Motor Losses for Single-phase and Continuous Motors 165 
LVIII. Particulars of 180- seat Trains with Continuous and Single-phase 

Equipments ......... 170 

LIX. Annual Costs for 180-seat Trains with Continuous and Single-phase 

Equipments .......... 172 

LX. Costs per Train-mile for 180-seat Train operating to a Schedule of 
26 ml ph, with one 20-second Stop per Mile, and aggregating 

62,400 Miles per Year 173 

LXI. Particulars of Weights of Motor-Coaches and Accessories used on 

Various Electric Railways ....... 191 

LXII. Average Values deduced from Data in Table LXI. .... 192 

LXTII. Values of the Percentage which the Weight of Electrical Equipment 

constitutes of Total Train Weight for Various Schedules . .194 
LXIV. Some Particulars of the Equipment on Eleven Railways employing the 

1200- volt Continuous Electricity System . . . . .196 



LIST OF FIGURES 

FIGURE PAGE 

1. Accelerating Portion of Speed-time Diagram, with Acceleration maintained 

constant at one ml phps ......... 1 

2. Accelerating Portions of Speed-time Diagram, showing how the Acceleration 

may be gradually increased up to its Final Value ..... 2 

3. Curves showing the Variation of the Acceleration with Time, corresponding to 

the Curves in Figs. 1 and 2 ........ 3 

4. Curve showing Distance travelled for the first 20 seconds of Run with the 

Various Initial Accelerations of the Curves of Fig. 3 . . . .4 

5. Portion of a Speed-time Diagram up to Point of Crest Speed .... 9 

6. Portion of a Speed-time Diagram up to Point of " Cut q^'" .... 10 

7. Portion of a Speed-time Diagram up to Point of Application of Brakes . . 11 

8. Complete Speed-time Diagram ......... 12 

9. Speed-time Diagram for an Electric Train operating over a Distance of 1120 m 14 

10. Area equal to that enclosed by the Curve in Fig. 9, and therefore representing 

the Distance covered during the Run ....... 14 

11. Speed-time Diagram for a Steam Train performing the same Journey as the 

Electric Train of Fig. 9 15 

12. Area equal to that enclosed by the Curve in Fig. 11, and therefore representing 

the Distance covered during the Run . . . . . . .15 

13. Initial Acceleration Periods of Speed-time Diagrams for the Electric and Steam 

Services of Figs. 9 and 11 ......... 16 

14. Distance-time Curves corresponding to Figs. 9 and 11 . . . . .17 

15. Relation of Schedule to Average Speed for Various Durations of Stop, for a 

1-mile Run from Start to Stop ........ 21 

16. Relation of Schedule to Average Speed for Various Lengths of Run with 

10-second and 30-second Stops ........ 22 

17. Curves showing Influence of Duration of Stop on the Schedule Speed for Runs 

of 0"5 and 1-mile Distance from Start to Stop ..... 23 

18. Hypothetical Speed-time Diagram, assuming no Track Friction ... 28 

19. Hypothetical Speed-time Diagram, taking Track Friction into account . . 31 

20. Diagram showing the Allocation of the Energy Input for a Service with an 

Average Distance of 0"30 Mile from Start to Stop, and a Schedule Speed of 

12-7 ml ph 38 

21 to 24. Curves giving the Percentage Allocation of the Total Input for Various 

Schedules under Normal Working Conditions .... 40-41 



xvi LIST OF FIGURES 

FIGURE PAGE 

25. Diagram showing Allotment of Total Input to 100-ton Train for Different 

Schedules, taken from the Curves of Figs. 21 to 24, and representing Actual 
Kuns 42 

26. Hypothetical Speed-time Diagram, with Acceleration and Deceleration of 1*0 

and 1*5 ml phps respectively, and no Track Friction .... 45 

27. Katio of Crest to Schedule Speed for Various Schedule Speeds and Euns, with 

Acceleration of I'O ml phps. Braking 1'5 ml phps. (Neglecting Decelera- 
tion during Coasting, i.e. assuming Frictionless Euns) .... 49 

28. Energy Consumption for Various Schedule Speeds and Euns under the Assumed 

Frictionless Conditions, and 100 per cent. Efficiency of Electrical Equip- 
ment. Acceleration 1*0 ml phps ; Braking 1*5 ml phps .... 51 

29. Speed-time Diagram for 0'5-mile Eun under Limiting Conditions. No Coasting 

Period and Minimum Acceleration and Deceleration .... 53 

30. Speed-time Diagram for 05-mile Eun with no Track Friction, Acceleration 

and Braking of 1*5 ml phps. ........ 54 

31. Speed-time Diagram for 1-mile, Eun covered at Schedule Speeds of 12, 18 and 24 

ml ph, with Constant Acceleration and Braking, and neglecting Train- 
friction ............ 57 

32. Speed-time Diagram for 1-mile Eun under Limiting Conditions. No Coasting 

Period; Acceleration and Deceleration of 1*0 and 1*5 ml phps respectively 59 

33. Speed- time Diagrams for 1-mile Eun covered at the Various Schedules indicated. 

No Train-friction . . . . . . . . . .61 

34. Curves of Train Consumption in w hr per ton-mile, assuming no Train-friction 

and 100 per cent. Efficiency of Equipment for 0"5-mile Eun and Various 
Schedule Speeds, with the Different Accelerations and Decelerations 
shown ............ 62 

35. Curves of Train Consumption in w hr per ton-mile, assuming no Train-friction 

and 100 per cent. Efficiency of Equipment for 1-mile Eun and Various 
Schedule Speeds, with the Different Accelerations and Decelerations shown 63 

36. Curves of Train Consumption in w hr per ton-mile, assuming no Train-friction 

and 100 per cent. Efficiency of Equipment for 2-mile Eun and Various 
Schedule Speeds, with the Different Accelerations and Decelerations shown G4 
37 and 38. Curves of Train Consumptions in w hr per ton and per ton-mile for 
Various Schedules, being Mean Curves from Figs. 34, 35 and 36, and 
therefore assuming no Train-friction and 100 per cent. Efficiency of 
Equipment ........... 65 

39. Lancashire and Yorkshire Kailway Speed-time Diagram for 10-mile Eun at 

Schedule Speed of 25-7 ml ph 68 

40. Distance-time Curve corresponding to Fig. 39 ...... 68 

41. Lancashire and Yorkshire Eailway Eepresentative Speed-time Diagram for 

1-32-mjle Eun at Schedule Speed of 30 ml ph 70 

42. Distance-time Curve corresponding to Fig. 41 ...... 70 

43. Eepresentative Efficiency Curves for a 150- hp Continuous-Electricity Eailway 

Motor on 500 volts (Parallel) and 250 volts (Series). (Curve E, Excluding 
Gear ; Curve G, Including Gear) ........ 72 

44. Eepresentative Speed-time Diagrams for Various Schedule Speeds and Euns 

under Working Conditions ......... 76 



LIST OF FIGURES xvii 

FIGURE PAGE 

45 aud 47. Curves giving Conservative Estimates of the Energy Consumption at 

the Train for Various Schedules under Normal Working Conditions (from 
calculations of Table XXVI., based on the Curves in Fig. 44) . 80 and 82 

46 and 48. Estimates of the Capacity of Equipment in Bated hp of Motors per Ton 

Weight of Train, necessary for operating Various Schedules under Normal 
Working Conditions 81 and 83 

49. Standard Four-coach Lancashire and Yorkshire Train . . . facing 86 

50. Typical Gradients on a Section of 0*48 mile (772 m) on the Central London 

Eailway ............ 87 

51. Typical Speed-time Diagram for 0-48-mile Run at Schedule Speed of 15-7 ml ph 89 

52. Curves of Efficiency at Various Outputs for G.E.66A Motors and Equipment . 90 

53. Outside Elevation of Central London Motor-Coach . . . facing 92 

54. Outside Elevation of Central London Trailer-Coach . . . . „ 92 

55. Interior View of Central Loudon Trailer-Coach . . . . . „ 92 

56. Average Speed-time Diagrams for Great Northern Piccadilly and Brompton 

Railway Tests A and B, from Values in Table XXXII 98 

57. Efficiency Curve for G.E.69B Railway Motor, 500 volt, 200 hp, as used on 

Great Northern Piccadilly and Brompton Railway ..... 102 

58. Outside Elevation of Great Northern Piccadilly and Brompton Railway Trailer- 

Coach .......... facing 104 

59. Interior View of Great Northern Piccadilly and Brompton Railway Trailer- 

Coach . . . . . . . . . . facing 104 

60. Grouping of the Over-all Efficiencies of Electrical Equipment for L. and Y.R., 

C.L.R. and G.N.P. and B.R., from Chapters V., VI. and VII. . . .105 

61. Determination of Acceleration and Power from Speed-time Diagram . .110 

62. Acceleration and Power-Curves deduced from the Speed-time Diagram in Fig. 61 111 

63. Curves showing Tendency of Train Resistance to decrease with Increased 

Weight of Train 122 

64. Curve showing Change of Tractive Resistance with Weight of Train as 

obtained from Results of Tests given in Table XLI. .... 125 

129 
135 
138 
139 
139 
140 
140 



65. Curves showing the Tractive Resistance for Trains of Various Weights . 

66. Speed-time Diagram for Run of One Mile at a Schedule Speed of 25 ml ph 

67. Current Input to each Motor for the Run indicated in Fig. 66 

68. Representation of Series Arrangement of the Eight Motors on the Train . 

69. Representation of Parallel Arrangement of the Eight Motors on the Train 

70. Current Input to the Entire Train for the Run indicated in Fig. 66 

71. Kilowatts Input to Train for the Run indicated in Fig. 66 . . . 

72. Showing Allocation of the Energy Input of the Run indicated in Fig. 66, with 

an Over-all Efficiency of Electrical Equipment of 70 per cent. . . . 141 

73. Current and Speed-Curves re-plotted from Figs. 66 and 67 . . . . 142 

74. Characteristic (ml ph) Speed-Curve of the Train obtained from Fig. 73 . .142 

75. Characteristic (rpm) Speed-Curve of the Motors ...... 143 

76. Plan of Electrified Portion of Midland Railway at Heysham .... 145 

77. Diagram of Gradients and Curves of Electrified Portion of Midland Railway at 

Heysham ............ 146 

78. Siemens Motor-Coach Complete ...... facing 152 

79. Westinghouse Motor-Coach Complete ....... 152 



XVlll 



LIST OF FIGURES 



FIGURE 

80 
81, 
82 
83, 



PAGE 
152 

153 
155 



View of Train consisting of Siemens Motor-Coach and Two Trailers facing 
Speed-Time Diagram for 3-43-miles Eun at an Average Speed of 33'3 ml ph . 
Curves relating to the Energy Input for the Run indicated in Fig. 81 
Characteristic Curves of the Siemens Motor on the Heysham Electrified 

Portion of the Midland Railway . . . . . . . . 1 56 

84. G.E.69B Series-wound Continuous Motor 161 

85 and 86. Curves showing Weights and Costs of a 180-seat Train for Various 

Schedule Speeds with One Stop per Mile . . . 175 and 176 

87. Curves showing the Acceleration in ml phps necessary to maintain Various 

Schedules for Several Distances between Stops . . . . .182 

88. W.E.51 Single-phase Motor 189 



LIST OF ABBREVIATIONS EMPLOYED. 

Foot, feet ft 

Feet per second per second ......... ft psps 

Horse-power ...... .... . . hp 

Inch ............. in 

Kilogram ............ kg 

Kilogram-meter ........... kg m 

Kilogram-meters per second . . . . . . . . . kg m ps 

Kilometer ............ km 

Kilometers per hour .......... km ph 

Kilowatt ............ kw 

Kilowatt-hour — Kelvin .......... kw hr 

Meter ............. m 

Meters per second . . . . . . . . . . . m ps 

Meters per second per second ......... m psps 

Miles per hour ........... ml ph 

Miles per hour per second ......... ml phps 

Watt-hour ............ w hr 

Watt-second ............ w sec 



ELECTRIC TRAINS 



CHAPTER I 



SPEED- TIME DIAGBAMS 

In making calculations relating to the electric propulsion of trains, 
one of the first steps consists in constructing " speed-time " diagrams.* 
A speed-time diagram is usually drawn with times, in seconds, from 
the instant of starting the train, as abscissae, and with the correspond- 
ing speeds, in miles per hour, as ordinates. Let us take the case of a 
passenger train operating under the average conditions which obtain 



2^ 



_^ 



e e /o /2 /^ /e 

77/rfe /n Sfeconds 



/a 20 



Fig. 1. — Accelerating Portion of Speed-time Diagram, with Acceleration maintained 

constant at one ml phps. 

on such lines as those of the Underground Electric Railways Co. of 
London, or of the Central London Railway. At the instant of switch- 
ing on the electricity, i.e. at the instant of starting, the speed is zero. 

* An excellent mathematical treatment of the subject of speed- time diagrams is 
given by C. 0. Mailloux, in a paper entitled "Notes on the Plotting of Speed-Time 
Curves," and read before the American Institute of Electrical Engineers (" Trans- 
actions," vol. xix. p. 901). 

B 



2 ELECTRIC TRAINS 

One second later the speed may be one mile per hour (one ml ph) 
or more. If, at the end of the first second, the train has acquired a 
speed of one ml ph, the average acceleration during the first second 
is said to have been one mile per hour per second (one ml phps). 
If this acceleration is maintained uniform for 20 seconds, the speed 
at the end of the 20th second will be 20 ml ph. For such a case the 
first part of the speed- time diagram is drawn as shown in Fig. 1. 
The acceleration will, in practice, vary from instant to instant. 



PJ. 






















K.ZO 






































^ 


^ 














.<^ 


^ 


^ 












»' 


^ 


j^ 


^ 












y^ 


^ c 


y 










^ 


^ 








y^ 













2 ^ 6 3 /O /Z /4' /<a 
77me /n /Seconds 



/a 20 



I^iG, 2. — Accelerating Portions of Speed-time Diagram, showing how the Accelera- 
tion may be gradually increased up to its Final Value. 
Curve a, Final Acceleration I'l ml phps. 
>> o, ,, ,, J- ^ ,, 

<< c, ., •• J. o II 



The train will usually start off with only comparatively moderate 
acceleration, otherwise discomfort would be experienced by the 
passengers. But by the end of a very few seconds such a train as 
that instanced will be accelerating at one ml phps, or thereabouts, 
and the maximum acceleration may be 1'5 ml phps, or even more. 
Thus the first part of the speed-time diagram is usually more like one 
of the curves in Fig. 2, which represent accelerations gradually 
increasing to 1*1, 1*2, and 1*5 ml phps for curves a, &, and c 
respectively. 

The corresponding instantaneous values of the acceleration are 
shown in Fig. 3. Curve d corresponds to the constant acceleration 
of Fig. 1, and curves a, &, and c correspond to the gradually increas- 
ing accelerations of curves a, h, and c respectively of Fig. 2. 



SPEED-TIME DIAGRAMS 3 

In all four cases, the speed at the end of the 20th second is 20 ml 
ph, the average acceleration being therefore, in each case, 1*0 ml 
phps. But, obviously, the distance covered in the 20 seconds is less 
in the last three cases than in the first case. In the first case (i,e. 

\ 



I.Z 



% 

^ 1.0 

I 

\0.8 



V 


























^ 
















1 










/ 


f 


^ 




^ f 












vX- 


J. 












/ 

3k— 


y 


T 


T 












f 


\ 


/ 














/ 


/ 


C 


















y 


















y 





















/4- /6 /e 20 



z 4^ e e /o /z 

Time /n ^econc^s 

Fig. 3. — Curves showing the Variation of the Acceleration with Time, corresponding 

to the Curves in Figs. 1 and 2. 

Fig. 1, and curve d of Fig, 3), the average speed during the 20 seconds 
is 10 ml ph, and the distance covered in the 20 seconds is — 

20 



3600 



X 10 = 0-0555 mile = 89-2 m.* 



In the case of curve a in Fig. 2, the average speed is 9*5 ml ph, and 
the distance covered is only — 

^^ X 9-5 = 0-0528 mile = 84*7 m. 
obOO 

In the four cases, the initial and final acceleration, the mean speed, 
and the distance covered during the first 20 seconds are set forth in 
Table I. 



* 1 mile = 1609 meters (1609 m). 
The reader will find that the most practicable course, pending the general introduction 
of the kilometer (km) as a substitute for the mile, is to express all considerable 
distances in miles, and all short distances in meters. While the meter is already 
extensively used, and is practically as familiar as the foot or the yard, it will take 
many years to supersede the mile by the kilometer. 



ELECTRIC TRAINS 



Table I. — Data obtained prom the Curves of Figs. 1 to 3. 



Curve of acceleration 


Acceleration (ml phps). 


Mean speed 
(ml ph). 


Distance 


(of Fig. 3). 


Initial. 


Final. 


Mean. 


covered (m). 


d . 

a . 
b . 
c 


1-00 
0-50 
0-31 
0-14 


1-00 
1-10 
1-20 
1-50 


1-00 
1-00 
1-00 
1-00 


10-0 
9-5 
8-3 
7-0 


89-2 
84-7 
74-1 
62-5 



The distances covered during the first 20 seconds are plotted as 
a function of the initial accelerations, in the curve of Fig. 4. From 



-^/OO 



I 

r 

I 

8 



^ 



eo 



60 



P 



eo 





























































^ 


^ 


— 


■*^ 


"^ 


> 












/ 






















/ 






















/ 


r 




















/ 


/ 






















/c 























































































































Q2 Q^ Qe QO 40 

/nJtia/ ^cce/erMion in mfphps. 



/.a 



Fig. 4. — Curve showing Distance travelled for the first 20 seconds of Run with the 
Various Initial Accelerations of the Curves of Fig. 3. 

this curve it will be seen that, so far as is consistent with other con- 
siderations, it is very important that the initial acceleration shall be 
fairly high, in order that the train may perform its journey in the 



SPEED-TIME DIAGRAMS 5 

shortest practicable time. The considerations standing in the way 
of a high initial acceleration are : — 

1. The Stress imposed on the Rolling Stock. — Thus the higher the 
acceleration employed, the stronger and heavier must be the rolling 
stock. 

2. The Comfort of the Passengers. — If, at the very first instant 
of starting, the acceleration is moderate, it can, after that, be 
rapidly increased to even 2 ml phps without undue discomfort 
to passengers, provided the alteration in the acceleration is accom- 
plished smoothly, i.e. uniformly. Consequently, consideration has to 
be given to the rate of accelerating the acceleration. But this is a 
refinement which, while it must be carefully kept in mind, need 
rarely concern us in preliminary calculations. 

3. The Effects on the Power House, the Line, and the Sub- 
Stations. — The higher the acceleration, the greater will be the 
instantaneous peaks of load on the system. With a large number 
of trains running on short headway, the peaks tend to overlap, and 
are consequently less noticeable, but with infrequent trains, these 
peaks of load constitute a serious objection to employing a high 
acceleration. 

4. The Effect on the Electrical Equipment on the Train. — The 

greater the acceleration, the greater is the instantaneous load on the 
train equipment, and the more severe are the conditions to which 
such parts as the commutators and brushes of the motors, and the 
contacts of the controllers or contactors, are subjected. Consequently, 
the employment of very high accelerations may in some instances 
necessitate heavier and more expensive electrical equipments than 
would otherwise be required. 

Notwithstanding these considerations, maximum accelerations 
well above one ml phps are commercially employed in the electrical 
operation of such trains as those on London's underground railways, 
as against accelerations of the order of 0'3 to 0*4 ml phps for 
equivalent steam trains. Mr. Mordey has analysed the conditions of 
operation of the electric trains on the Liverpool Overhead Kail way, 
and has shown that on certain occasions the acceleration, 2 or 3 
seconds after starting, reached 2*8 ml phps.* In some tests, made 
in America by the General Electric Co. with a 65-ton train, the 
average acceleration during the first 5 seconds worked out at nearly 
3 ml phps.f But even so relatively low an acceleration as 1*5 ml 
phps has been criticised | as involving expensive and heavy rolling 

♦ " Proceedings, Institution of Civil Engineers," February, 1902. 

t "Transactions, American Institute of Electrical Engineers," vol. xix. p. 844. 

X Mr. Roger Smith, in Railway Gazette, February 5, 1909, p. 170. 



6 ELECTRIC TRAINS 

stock construction to withstand the attendant stresses. Taking it all 
in all, however, it may be said that electrically-propelled passenger 
trains on well-built railways will usually be operated with a maximum 
of commercial advantage, when the average acceleration, during 
at least the first 10 seconds from starting, is from 0*6 to 1'5 ml phps. 
For reasons which will be better understood at a later stage, the lower ol 
these accelerations will be approached when the distance between 
stops is greater and the schedule speed lower, whereas, for short 
distances between stops, high schedule speeds are only possible when 
the higher of these accelerations is approached. The customary 
accelerations of steam-hauled passenger trains range from 0*2 to 0*4 
ml phps.* 

On the Continent, train speeds are expressed in km ph (kilo- 
meters per hour), and accelerations in m psps (meters per second 
per second). In Great Britain, train speeds are expressed in ml ph, 
and accelerations are expressed either in ml phps (miles per hour 
per second), or in ft psps (feet per second per second). The use, 
sometimes of the one and sometimes of the other of these last two 
units, when expressiug accelerations, is troublesome, but it seems 
unlikely that any uniformity will be arrived at in the near future. 
It is beyond all question more convenient for practical railway calcu- 
lations, to express accelerations in ml phps, since this leads to great 
convenience in calculating. Thus, if a train has accelerated at the 
average rate of 1'2 ml phps for 9 seconds, its speed at the end of 
the 9th second is — 

9x1-2= 10-8 ml ph. 

In Table II. are given, for various units, equivalent values of speeds 
and accelerations. 

* " Comparative Acceleration Tests with Steam Locomotive and Electric Motor- 
cars," by B. J. Arnold and W. B. Potter. " Transactions of the American Institute 
of Electrical Engineers," vol. xix. p. 833. 



SPEED-TIME DIAGRAMS 

Table II. — Conversion Table for Speed and Acceleration. 



Miles per 


Feet per 


KUometers 


Meters per 


T3 


Miles per 


Feet per 


Kilometers 


Meters per 


hour 


second. 


per hour 


second 


0) 


hour 


second 


per hour 


second 


(ml ph). 


(ftps). 


(km ph). 


(m ps). 


P. 

a 


(ml ph). 


(ft ps). 


(km ph). 


(m ps). 


Miles per 


Feet per 


Kilometers 


Meters per 


MUes per 


Feet per 


Kilometers 


Meters per 


hour per 


sec per 


per hr per 


sec per 


(-1 


hour per 


sec per 


per hr per 


sec per 


sec. 


sec. 


sec. 


sec. 


V 


sec. 


sec. 


sec. 


sec. 


(ml phps). 


(ft psps). 


(km phps). 


(m psps). 




(ml phps). 


(ft psps). 


(km phps). 


(m psps). 


0-1 


0-1467 


0-1609 


0-0447 




10 


14-67 


16-09 


4-470 


0-1364 


0-2 


0-2194 


0-0610 




10-23 


15 


16-46 


4-572 


0-2 


0-2934 


0-3218 


0-0894 




12 


17-60 


19-31 


5-36 


0-2728 


0-4 


0-4388 


0-1219 




12-42 


18-22 


20 


5-55 


0-3 


0-440 


0-4827 


0-1341 




13-64 


20 


21-94 


6-10 


0-4 


0-5868 


0-6436 


0-1788 




14 


20-53 


22-53 


6-26 


0-4091 


0-6 


0-6584 


0-1829 




15-53 


22-78 


25 


6-94 


0-5 


0-7335 


0-8045 


0-2235 




16 


23-47 


25-75 


7-15 


0-5454 


0-8 


0-8778 


0-2438 




17-05 


25 


27-43 


7-62 


0-6 


0-880 


0-9654 


0-2682 




18 


26-40 


28-97 


8-05 


0-6214 


0-9114 


1 


0-2778 




18-63 


27-34 


30 


8-33 


0-6818 


1 


1-097 


0-3050 




20 


29-33 


32-19 


8-94 


0-7 


1-027 


1-126 


0-3129 




20-46 


30 


32-91 


9-14 


0*8 


1-172 


1-287 


0-3576 




21-75 


31-90 


35 


9-72 


0-8182 


1-2 


1-316 


0-3658 




22 


32-27 


35-40 


9-83 


0-9 


1-320 


1-448 


0-4023 




23-86 


35 


38-40 


10-67 


0-9545 


1-4 


1-536 


0-4267 




24 


35-2 


38-60 


10-73 


10 


1-467 


1-609 


0-447 




24-85 


36-45 


40 


11-10 


1-023 


1-5 


1-646 


0-457 




26 


38-13 


41-84 


11-62 


1-242 


1-822 


20 


0-556 




27-28 


40 


43-88 


12-19 


1*25 


1-833 


2-012 


0-559 




27-96 


41-01 


45 


12-50 


1-364 


2 


2-194 


0-610 




28 


41-06 


45-06 


12-51 


1-5 


2-20 


2-414 


0-671 




30 


44-0 


48-28 


13-41 


1-705 


2-5 


2-743 


0-762 




30-68 


45 


49-38 


13-72 


1-75 


2-567 


2-816 


0-782 




31-06 


45-56 


50 


13-88 


1-863 


2-733 


30 


0-833 




32 


46-93 


51-50 


14-30 


20 


2-930 


3-219 


0-894 




34 


49-87 


54-72 


15-20 


2-046 


30 


3-291 


0-914 




34-09 


50 


54-86 


15-24 


2-25 


3-30 


3-622 


1-006 




34-18 


50-12 


55 


15-27 


2-386 


3*5 


3-840 


1-067 




36 


52-80 


57-94 


16-09 


2-484 


3-644 


40 


1-111 




37-27 


54-67 


60 


16-66 


2-5 


3-668 


4-023 


1-118 




37-5 


55 


60-35 


16-76 


2-728 


40 


4-388 


1-219 




38 


55-73 


61-15 


16-99 


2-75 


4-034 


4-426 


1-229 




40 


58-67 


64-37 


17-88 


30 


4-40 


4-828 


1-341 




40-40 


59-24 


65 


18-06 


3-068 


4*5 


4-938 


1-372 




40-91 


60 


65-84 


18-29 


3-107 


4-557 


50 


1-389 




42 


61-60 


67-59 


18-78 


3-25 


4-767 


5-230 


1-453 




43-49 


63-79 


70 


19-43 


3-409 


50 


5-486 


1-524 




44 


64-53 


70-81 


19-67 


3-5 


5-13 


5-633 


1-565 




44-32 


65 


71-32 


19-81 


3-728 


5-47 


60 


1-667 




46 


67-47 


74-03 


20-56 


3-75 


5-5 


6-035 


1-676 




46-61 


68-35 


75 


20-83 


40 


5-87 


6-437 


1-788 




47-73 


70 


76-81 


21-34 


6 


8-8 


9-656 


2-682 




48 


70-40 


77-25 


21-46 


6-21 


9-11 


10 


2-778 




49-6 


72-90 


80 


22-21 


6-82 


10 


10-97 


3-048 




60 


73-33 


80-47 


22-35 


8 


11-73 


12-87 


3-576 




61-14 


75 


82-30 


22-86 


9-32 


13-67 


15 


4-167 




52 


76-27 


83-68 


23-25 



ELECTRIC TRAINS 



Table II. — Conversion Table foe 


Speed and ^ 


A.CCELEEATION — continued. 


Miles per 


Feet per 


Kilometers 


Meters per 


V, 


Miles per 


Feet per 


Kilometers 


Meters per 


hour 


second 


per hour 


second 


0) 


hour 


second 


per hour 


second 


(ml ph). 


(ft pa). 


(km ph). 


(m ps). 


^ 


(ml ph). 


(ft ps). 


(km ph). 


(m ps). 


Miles per 


Feet per 


Kilometers 


Meters per 


i 


Miles per 


Feet per 


Kilometers 


Meters per 


hour per 


sec per 


per hr per 


sec per 




hour per 


sec per 


p«r hr per 


sec per 


sec. 


sec. 


sec. 


sec. 


o 


sec. 


sec. 


sec. 


sec. 


(ml phps). 


(ft psps). 


(km phps). 


(m psps). 


s 

u 

^ 


(ml phps). 


(ft psps). 


(km phps). 


(m psps). 


62-82 


77-47 


85 


23-50 




90 


132-0 


144-8 


40-23 


54 


79-20 


86-90 


24-14 




90-2 


132-1 


145 


40-28 


64-55 


80 


87-78 


24-38 




92 


134-9 


148-0 


41-13 


65-61 


82-01 


90 


24-99 




92-05 


185 


148-1 


41-15 


56 


82-13 


90-12 


25-03 




93-18 


136-7 


150 


41-64 


67-95 


85 


93-27 


25-91 




94 


137-9 


151-3 


42-02 


58 


85-07 


93-34 


25-93 




95-46 


140 


153-6 


42-67 


69-03 


86-68 


95 


26-39 




96 


140-8 


154-5 


42-91 


60 


88-0 


96-56 


26-82 




96-3 


141-3 


155 


43-06 


61-36 


90 


98-76 


27-43 




98 


143-7 


157-7 


43-81 


62 


90-93 


99-78 


27-72 




98-9 


145 


159-1 


44-19 


62-14 


91-14 


100 


27-78 




99-4 


145-8 


160 


44-43 


64 


93-87 


103-0 


28-61 




100 


146-7 


160-9 


44-70 


64-77 


95 


104-2 


28-96 




102 


149-6 


164-2 


45-60 


65-24 


96-7 


105 


29-17 




102-3 


160 


164-6 


45-72 


66 


96-8 


106-2 


29-60 




102-5 


150-4 


165 


45-83 


68 


99-7 


109-4 


30-40 




104 


152-6 


167-4 


46-49 


68-18 


100 


109-7 


30-48 




105-6 


164-9 


170 


47-22 


68-34 


100-2 


JiO 


30-54 




106-7 


155 


170-1 


47-24 


70 


102-7 


112-7 


31-29 




106 


155-5 


170-6 


47-39 


71-46 


104-8 


115 


31-94 




108 


168-4 


173-8 


48-28 


71-69 


105 


115-2 


32-00 




108-7 


159-6 


175 


48-61 


72 


105-6 


116-9 


32-19 




109-1 


160 


175-6 


48-77 


74 


108-6 


119-1 


33-08 




110 


161-3 


177-0 


49-17 


74-65 


109-3 


120 


33-32 




111-8 


164-0 


180 


50 


75-0 


110 


120-7 


33-53 




112 


164-3 


180-2 


60-07 


76 


111-5 


122-3 


33-97 




112-6 


165 


181-1 


60-29 


77-67 


113-9 


125 


34-72 




114 


167-2 


183-5 


60-96 


78 


114-4 


125-5 


34-87 




115 


168-6 


185 


51-39 


78-41 


115 


126-2 


36-05 




116-9 


170 


186-5 


51-81 


80 


117-3 


128-7 


36-76 




116 


170-1 


186-7 


51-86 


80-77 


118-4 


130 


36-10 




118 


173-1 


189-9 


52-75 


81-82 


120 


131-7 


36-67 




118-1 


173-2 


190 


52-78 


82 


120-3 


132-0 


36-66 




119-3 


175 


192-1 


53-34 


83-89 


123-0 


135 


37-60 




120 


176-0 


193-1 


63-64 


84 


123-2 


136-2 


37-56 




121-2 


177-7 


195 


64-17 


86-23 


125 


137-2 


38-10 




122 


178-9 


196-3 


64-54 


86 


126-1 


138-4 


38-44 




122-7 


180 


197-5 


54-86 


86-98 


127-6 


140 


38-87 




124 


181-9 


199-6 


56-43 


88 


129-1 


141-6 


39-34 




124-3 


182-3 


200 


66-56 


88-64 


130 


142-6 


39-62 


125 


183-3 


201-2 


55-88 



In practical calculations it is rarely necessary to take into account 
the slight deviations from a constant value of the acceleration during 
the first few seconds after starting the train. This first section of the 



SPEED-TIME DIAGRAMS 9 

speed-time diagram may consequently often be taken as practically 
a straight line. The straight-line portion is followed by a curved 
portion corresponding to a rapidly decreasing acceleration until, 
finally, a substantially constant speed is reached. This is shown in 
Fig. 5. 

It is seen that in the example chosen, the substantially constant 
speed may be considered to have been attained at the end of 70 
seconds, and is of the value of 35 ml ph. This maximum speed 

SO 



4C 









\.20 



/O 













































































^ 


^ 
















J 


y 


















i 


/ 




















/ 


1 




















/ 




















1 






















/ 
























^ 


7 


A 





(Si 





a 


t? 


/c 


V 



Time //? Seconds 

I Fig. 5. — Portion of a Speed-time Diagram up to Point of Crest Speed. 



attained during any run may be designated as the crest speed. The 
second section of the speed-time diagram, i.e, the section extending, 
in this case, from the 20th to the 70th second, is, for reasons which 
will be apparent later, termed the section corresponding to " running 
on the motor characteristic." In our example, the " straight-line " 
acceleration lasted for 20 seconds and was of the value of one ml phps. 
The " motor characteristic " acceleration lasted for 50 seconds and 
had the average value of — 

^^ ~ ^^ = 0-30 ml phps. 
50 



10 



ELECTRIC TRAINS 



The shape of the portion of the curve corresponding to running 
on the " motor characteristic " is dependent on the design and 
type of the motor, and is not amenable to simple calculation.* If 
electricity continues to be supplied to the motors, the train will 
continue to accelerate slightly for a considerable time — say two 
to five minutes — and will not reach a constant speed until the 
power delivered to the wheels equals the power required to overcome 
the resistance to motion (i.e, the train-friction) at that speed. It is 
therefore seen that this constant speed running, only applies to 



GO 






















A/\ 






















40 

\ 

^ 30 
















►-H 


1 














■^ 




w 








/ 


/ 
















A 


A 
















\S^ 20 




/ 


1 
















//I 


1 


/ 


















10 






















/ 



















20 ^ ^ SO 

TT/ne /n Seconcfs 



/CO 



Fig. 6. — Portion of a Speed-time Diagram up to Point of " Cut off." 

relatively long runs, but, in order to introduce into our speed-time 
diagram a part representative of this condition, we will assume that 
a substantially constant speed has been attained, and the train may 
be regarded as continuing to run at this speed for a short time, which, 
in the present instance, we may take as 10 seconds. Consequently, 
the shape of the speed- time diagram up to the 80 th second from 
starting the train is that shown in Fig. 6. At this point, the electricity 
is cut off and the train is allowed to decrease in speed under the 

♦ The " motor characteristic " is discussed more fully in Chapter X. p. 132. 



SPEED-TIME DIAGRAMS 



II 



retarding influence of friction. The train is said to " coast " or 
" drift." This " coasting " section of the speed-time diagram will 
usually be maintained until the train has nearly arrived at the point 
of the route where it is desired that it should stop. Let us assume, 
for our example, that the train coasts for 20 seconds. At the con- 
clusion of the 20 seconds the speed will have fallen a small amount, 
the precise value of which is dependent upon the train-friction in 
any particular case. The fall in speed, with good rolling stock and 
track, is usually of the order of some 07 ml phps ; i.e. the train- 
friction occasions a deceleration of 0*07 ml phps. Consequently, in 
our example, the speed at the end of the 100th second, i.e. at the 
end of the coasting section, will be — 



as shown in Fig. 7. 



(35 - 20 X 0-07 =)33-6 mlph, 



SC 



40 






or 



30 



10 



<►— <l 



20 ^ 60 do /OO /20 /40 

Time /n %3econds 

Fig. 7. — Portion of a Speed-time Diagram up to point of A'^licxiiion of Brakes. 



The next and final section of the speed-time diagram is that 
during which the brakes are applied until the train is brought to rest. 
Let us, for example, consider that the brakes are applied with such 
a pressure as to occasion a deceleration of 1'5 ml phps. This is a 
deceleration which, if maintained uniform, does not involve discomfort 
to passengers. The duration of the " braking " section of the speed- 

(QQ.f? \ 

-— = j22'5 seconds, as shown in Fig. 8. In 

normal services of city and suburban passenger trains, the brake 



12 



ELECTRIC TRAINS 



system is usually so operated as to occasion a deceleration of from 
1 to 2 ml phps. The present tendency is toward still higher values 
of the deceleration. 




20 ^ eo GO /CX> /20 

T^e in 'Seconds 

Fig. 8. — Complete Speed-time Diagram. 



/40 



We now have the complete speed-time diagram. The run from 
start to stop has been accomplished in 122*5 seconds. The distance 
traversed may be obtained by the steps shown in Table III. 

Table III. — Data obtained fbom the Speed-time Diagram of Fig. 8. 



Section. 


Duration 
(seconds). 


Mean speed 
(ml ph). 


Distance covered. 


(mile). 


(m). 


" Straight-line " acceleration . 
" Motor-characteristic " . 
Constant speed . . . ' . 
Coasting (or drifting) 
Braking ...... 


20 
50 
10 
20 
22-5 


100 
30-2 
35-0 
34-3 
16-8 


00555 

0-420 

0-0975 

0-190 

0-1050 


89-2 
675-0 
156-5 
305-5 

168-8 


Total ..... 


122-5 


— 


0-868 


1395 



Thus, a total distance of 0868 mile is covered in 122*5 seconds. 
The average speed is consequently — Ivi 

3600 X 0-868 o..fr 1 t, 
122-5 = ^^^ ^^ P^- 



SPEED-TIME DIAGRAMS 13 

The mean speed from start to stop is termed the average speed. 
But the mean speed between two successive starts, i.e. the mean 
speed including the time during which the train is at rest, is termed 
the schedule speed. Thus, in the case of our example, if a 20-second 
stop is made at each station, then the time elapsing between successive 
starts (or stops) is 122'5 + 20 = 142*5 seconds, and the schedule speed 
is — 

3600 X 0-868 01.0 11. 
142-5 = ^^^ ^^ P^- 

As characteristic of the particular speed-time diagram which we have 
taken for our example, we have — 

Crest speed 35*0 ml ph. 

Average speed 25*5 „ 

Schedule „ 21-9 „ 

It is interesting to observe that in order to obtain a schedule speed 
of 21*9 ml ph it has been necessary to employ a crest speed of 35*0 
ml ph. The crest speed is, in this case, 1'60 times the schedule 
speed. The crest speed is also 1*37 times the average speed. 

The value of the ratio of the crest to the average speed is of great 
interest, and is a rough measure of the severity of a service. The 
higher the speed and the shorter the distance between stops, the 
greater must be the ratio of the crest to the average speed, and the 
more severe is the service. The ratio of the crest to the average 
speed does not depend exclusively on the average speed and the 
distance between stops, but also depends on the acceleration during 
starting and the deceleration during braking, the ratio being lower 
the higher the acceleration and deceleration. The subject of the 
ratio of the crest to the average speed is considered thoroughly in 
subsequent chapters. 

In the speed-time diagram which has been employed as an 
example in the preceding pages (see Fig. 8), straight-line acceleration 
has been maintained up to 57 per cent, of the crest speed. This 
particular diagram has been convenient in serving the purposes of 
explaining the fundamental principles involved, but in practice 
straight-line acceleration often extends up to only some 50 per cent., 
or even less, of the crest speed. Moreover, for a service with frequent 
stops and high schedule speed, there is seldom an interval of running 
at constant speed. For such a service, certain rational assumptions 
are made as to the accelerating, coasting, and braking rates, and 
these are employed in constructing a representative speed-time 
diagram. In operating the train, it is usually economical to cut off 
the electricity immediately on the attainment of the crest speed 
given in the representative diagram. This speed will usually be well 



14 



ELECTRIC TRAINS 



below the maximum speed which would be attained by runniDg 
longer on the " motor curve," but such relations depend on many 
conditions, which have to be taken into account when specifying the 
equipment for any particular service. 

A speed-time diagram is shown in Fig. 9 which is typical for 









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Fig. 9.— Speed-time Diagram for an Electric Train operating over a Distance o 

1120 m. 



^///////////////////////////////////// 






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^////////////// ////////////////////////. 



V 



Dumtion of ffun 'llOsccoixeh *j 



Fig. 10. — Area equal to that enclosed by the Diagram in Fig. 9, and therefore 
representing the Distance covered during the Run. 



electric train operation under rather severe conditions, and which has 
no interval of running at constant speed, electricity being cut off 
48 seconds from the start, and the train allowed to drift for the 
next 45 seconds, with consequent decrease in speed due to train 
resistance. The brakes are then applied, and the train is brought to 
rest 110 seconds from the instant of starting. 



SPEED-TIME DIAGRAMS 



15 



In Fig. 11 is given a speed- time diagram for a steam train 
operating over a route of the same number of stops per mile (that is, 
with the same distance between stops). The low acceleration shown 
in the diagram is typical of a steam-hauled train. The crest speed is 
the same in Fig. 11 as in Fig. 9, but, as a consequence of the lower 



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/o 20 ^ ^ 50 00 JO so eo /oo //o /zo /30 MO ^50 
77m c in seconds 

Fig. 11. —Speed-time Diagram for a Steam Train performing the same Journey as 

the Electric Train of Fig. 9. 




Ourabion of /fun 'MOseconds- 



FiG. 12. — Area equal to that enclosed by the Diagram in Fig. 11, and therefore 
representing the Distance covered during the Run. 



acceleration of the steam train, its speed from start to stop, ix. its 
average speed, is much less than that of the electric train. 

The distance from start to stop may be found from a speed-time 
diagram by measuring its area, either by means of a planimeter or 
else by obtaining the average ordinate for the entire diagram (which 
is, of course, equal to the average speed, in ml ph, from start to stop), 
and multiplying by the time, expressed with the hour as unit. Thus, 
from the diagrams of Figs. 9 and 11, the data set forth in Table IV. 
may be obtained — 



i6 



ELECTRIC TRAINS 

Table IV. — Data obtained from Figs. 9 and 11. 



Average speed (ml ph) a 

Time from start to stop (seconds) 

„ „ (hour) 6 

Distance from start to stop (mile), a x & 
Do. (m) a X 6 X 1609 .... 
Crest speed (ml ph) .... 
Batio of crest to average speed 



Electric Train 


Steam Train 


(Fig. 9). 


(Fig. 11). 


22-8 


17-9 


110 


140 


0-0306 


0-0389 


0-698 


0-698 


1120 


1120 


30 


30 


1-32 


1-68 



20 



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7?/ne in 'ffeco/id& 



20 



Fig. 13. — Initial Acceleration Periods of Speed-time Diagrams for the Electric and 

Steam Services of Figs. 9 and 11. 



SPEED-TIME DIAGRAMS 



17 



In Figs. 10 and 12 the two rectangles are respectively equal to 
the areas of the speed- time diagrams of Figs. 9 and 11. In these 
rectangles the ordinates equal the average speeds and the abscissae 
equal the times required to cover the distance from start to stop. 
Since the distance is the same in the two cases, the areas of these 
two rectangles are equal. Obviously, then, the time (represented by 
the length of the base of the rectangle) which is required to traverse 
a given distance is inversely proportional to the average speed 
(represented by the height of the rectangle) maintained during the 
journey. 

The distance from the start which has been traversed up to any 
particular instant of the journey may be obtained by estimating 



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Fig. 14. — Distance-time Curves corresponding to Figs. 9 and 11. 



the area of that portion of the diagram lying to the left of the 
ordinate corresponding to the instant in question. Thus, the dis- 
tances covered during the first 20 seconds from the start in Figs. 9 
and 11 are equal to the two areas shown in Fig. 13. The average 
ordinates of these two areas are respectively 11*2 and 4*0, i.e, 
the average speeds for the first 20 seconds from the start are 
respectively — 

For Electricity . . . . 11*2 ml ph 
„ Steam .... 4*0 ml ph. 

c 



1 8 ELECTRIC TRAINS 

The corresponding distances are — 

20 
For Electricity, 11-2 x gg^ X 1609 = 100 m 

20 
„ Steam, 4*0 X ^^7^ X 1609 = 36 m. 

obOO 

In this way, curves may be derived in which distances (in m) 
are plotted as ordinates against time (in seconds) as abscissae. The 
distance-time curves corresponding to the speed-time diagrams of 
Figs. 9 and 11 are plotted in Fig. 14. 

Examples. 

1. If a train is accelerated for 8 seconds at the rate of 1-2 ml phps, what is its 
speed at the end of the 8th second ? Ans. 9-6 ml ph. 

2. What must be the average acceleration of a train for the first 20 seconds from 
the start if its speed at the end of that time is 18 ml ph ? Ans. 0*9 ml phps. 

3. What accelerations are usually employed on electric city and suburban rail- 
ways operating with frequent stops? Ans. 0*8 to 1*5 ml phps. 

4. Ditto when the trains are hauled by steam locomotives ? 

Ans. 0*3 to 0*6 ml phps. 

5. What circumstances limit in practice the acceleration of electric city and 
suburban trains ? Ans. (As in text, p. 5). 

6. What is the customary rate of braking of electric trains ? 

Ans. 1*5 to 2*0 ml phps. 

7. What deceleration is caused on a good level permanent way by the train 
friction when the supply of electricity is cut off and the train drifts ? 

Ans. Some 0-07 to 0-09 ml phps. 

8. If in a certain instance train friction occasions a deceleration of 0*07 ml 
phps, and if, when the train is running at a speed of 30 ml ph, the supply of 
electricity is cut off, what will be the speed of the train after it has " drifted " for 
50 seconds ? Ans. 26*5 ml ph. 

9. For how many seconds would the train run, assuming the deceleration remained 
constant, if it were allowed to drift until it came to rest ? Ans. 429 seconds. 

10. What distance would it cover in this time ? 

Ans. 1-79 mile (i.e. 2880 m). 

11. When a train is running at a speed of 20 ml ph at the moment the brakes 
are applied, and it is desired to bring the train to rest in 15 seconds, what average 
deceleration must be occasioned by the brakes ? Ans. 1*33 ml phps. 

12. What distance will be covered, in this case, during the 15 seconds of appli- 
cation of the brakes? ^ Ans. 0*042 mile (i.e. 67-6 m).^ 

13. When the schedule speed of a train is 15 ml ph and there is 1 stop per mile, 
and if each stop is of 20 seconds' duration, what is the average speed of the train ? 

Ans. 16'4 ml ph. 

14. Plot a diagram, with distances as ordinates and times from start as abscissae, 
corresponding to the speed-time diagram of Fig. 8. 

15. If, instead of as in Fig. 8, the deceleration from the 100th second until the train 
came to rest had been maintained at the constant value of 0*50 ml phps, (i.) what would 
have been the duration of the journey, from start to stop, in seconds? (ii.) What 
distance would have been covered ? (iii.) What would have been the average speed ? 

Ans. (i.) 167-3 seconds; (ii.) 1*077 mile (i.e. 1730 m) ; (iii.) 23-3 ml ph. 

16. Plot the complete speed-time diagram and also a distance-time curve 
corresponding to the conditions of the last question. 



CHAPTER II 



THE INFLUENCE OF TEE NUMBER OF STOPS PER MILE, 
AND OF TEE DURATION OF FACE STOP 

It is of the utmost importance, as affecting the earning capacity of a 
railway, that, for short and fast runs, the stops at stations shall be 
of the shortest practicable duration. To illustrate the importance of 
this point, let us consider the case of a train stopping every half mile, 
and operated with an average speed of 22 ml ph. If the stops were 
of seconds duration, the schedule speed would be 22 ml ph. 

The train stops every half mile. Consequently, the time occupied 
by a single run from start to stop is — 

0*5 

22 X 3600 = 82 seconds. 

If the duration of each stop is 10 seconds, then the time from start to 
start is— 82 + 10 = 92 seconds, 

and the schedule speed will be only — 

oo 

^ X 22 =: 19-6 ml ph. 
With 20-second stops the schedule speed will be reduced to — 

oo 

^ X 22 = 17-7 ml ph. 

Making similar calculations for stops of other durations, we arrive at 
the values set forth in Table V. — 

Table V. — Influence op Dueation op Stop on the Schedule Speed for an 
Average Speed op 22 ml ph, and for a Length op Run op 0*5 Mile. 











Percentage by 


Average speed 
(ml ph). 


Length of run 
(mile). 


Duration of stop 
(seconds). 


Schedule speed 
(ml ph). 


which the schedule 

speed is less than 

the average speed 

(per cent.). 


22 


0-5 





22-0 





22 


0-5 


10 


19-6 


11-0 


22 


0-5 


20 


17-7 


19-5 


22 


0-5 


30 


16-1 


26-8 


22 


0-5 


40 


14-8 


32-7 


22 


05 


50 


13-7 


37-7 


22 


0-5 


60 


12-7 


42-3 



19 



20 



ELECTRIC TRAINS 



With less frequent stops, i.e, with longer runs, the influence for the 
same average speed is much less pronounced. Thus, for 1 stop per 
mile, and an average speed of 22 ml ph, the results are shown in 
Table VI.— 

Table VI. — Influence of Dueation of Stop on the Schedule Speed for an 
Average Speed op 22 ml ph, and for a Length of Run of 1 Mile. 











Percentage by 


Average speed 
(ml ph). 


Length of rua 
(mile). 


Duration of stop 
(seconds). 


Schedule speed 
(ml ph). 


which the schedule 

speed is less than 

the average speed 

(per cent.). 


22 


10 





220 





22 


I'O 


10 


20-8 


5-5 


22 


10 


20 


19-6 


11-0 


22 


1-0 


30 


18-6 


15-5 


22 


1-0 


40 


17-7 


19-5 


22 


1-0 


50 


16-9 


23-2 


22 


10 


60 


161 


26-8 



The effect is also less serious the lower the average speed. Thus, with 
2 stops per mile, and an average speed of only 11 ml ph, the results 
are as shown in Table VII. — 

Table VII. — Influence of Duration of Stop on the Schedule Speed for an 
Average Speed of 11 ml ph, and for a Length of Run of 0*5 Mile. 



Average speed 
(ml ph). 


Length of run 
(mile). 


Duration of stop 
(seconds). 


Schedule speed 
(ml ph). 


Percentage by 

which the schedule 

speed is less than 

the average speed 

(per cent.). 


11 
11 
11 
11 
11 
11 
11 


0'5 
0-5 
0-5 
0-5 
0-5 
0-5 
05 



10 

20 
30 
40 
60 
60 


11-0 
10-4 
9-80 
9-30 
8-85 
8-45 
8-05 




5-5 
110 
15-5 
19-5 
23-2 
26-8 



In Fig. 15 are plotted, for various durations of stop, curves with 
schedule speeds as ordinates and average speeds as abscissae, for a 
1-mile run from start to stop. From these curves we see that while, 
with 10 -second stops, a schedule speed of 25 "0 ml ph requires an 
average speed of 27*0 ml ph, the corresponding average speed when the 
stops are of 30 seconds' duration is 31'5 ml ph. In Fig. 16 ordinates 
and abscissae still represent respectively schedule and average speeds, 
but each curve relates to some stated distance between stations. The 



INFLUENCE OF STOPS PER MILE 



21 



full-line curves all relate to 10-second stops, and the dotted line curves 
all relate to 30-second stops. 

It has been found by experience that for such cases as the London 
underground railways the average duration of stop need not exceed 



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Fig. 15. — Eelation of Schedule to Average Speed for Various Durations of Stop 
for a 1-mile Eun from Start to Stop. 

20 seconds ; at certain stations and times the stops must be longer, at 
others they may be shorter. 

The values in Tables V., VL, and VIL, and the curves in Figs. 15 
and 16, have been derived by starting from a given average speed and 
calculating the schedule speed. The reverse process, where the required 
schedule speed is given, and it is desired to ascertain the corresponding 



22 



ELECTRIC TRAINS 



average speed, may be carried out by reading off the values from curves 
such as those of Figs. 15 and 16, or by calculations of the following 
type. 



3- 



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y?yeraffe Speed /n m/jbh 



36 



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Fig. 16. — Kelation of Schedule to Average Speed for Various Lengths of Run 
with 10-second and 30-second Stops. 
10 seconds ........ Full line curves. 

30 seconds ........ Dotted line curves. 



Take the case of a schedule speed of 15 ml ph and one stop per 
mile. The time from start to start will be — 

-zr-^ ^ = 240 seconds. 

15 X 1 

With a 10-second stop, the time from start to sto'p must be — 

240 - 10 = 230 seconds. 

Consequently, the average speed is — 

^oQ X 15 = 15'7 ml ph. 



INFLUENCE OF STOPS PER MILE 



23 



For a given schedule speed, the number of stops per mile constitutes 
a very important factor as bearing upon the severity of the service, 
owing to the extent to which it affects the ratio of the crest to the 
average speed, and also (as we shall see in following chapters) the 
energy consumption per ton-mile. 

It is profitable at this point to anticipate for a moment and draw 
attention to the two curves in Fig. 17. These curves relate respectively 
to runs of 0*5 mile and 1 mile between stations, and show the 
dependence of the highest schedule speed attainable in practice on 
the duration of each stop. The curves are based on 1'5 ml phps as 
the mean of the acceleration and deceleration, and the crest speed is 



so 



I 

"§ 20 
10 



































































































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— 


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/^urat^/on (^ Sdops m ^seconds 



2a 



Fig. 17. — Curves showing Influence of Duration of Stop on the Schedule Speed 
for Runs of 0'5 and l-mile Distance from Start to Stop. 



taken as about 1*7 times the average speed. These, while attainable, 
are rather extreme conditions, and commercial limitations would 
usually lead to decreasing by from 10 per cent, to 20 per cent, the 
values to which the curves are plotted. The curves serve, however, 
to show very clearly the importance of operating trains for a city 
and suburban service with as brief stops as possible at stations. 

It is usually assumed that " moving platform " schemes of pas- 
senger transportation are impracticable. While grave difficulties are, 
of course, inherent to such schemes, there are, nevertheless, strong 
grounds for giving them careful consideration. Thus, from Fig. 17 
we see that for 0'5-mile runs between stops, and with 20-second 
stops, the highest practicable schedule speed is some 20 ml ph. As a 



24 ELECTRIC TRAINS 

matter of fact, the co7nmercial limit is more like 17 ml ph. A train 
operating to a schedule speed of 17 ml ph makes — 

17 

^r^ = 34 stops per hour. 

Consequently, the train is at rest for (34 X 20 = )680 seconds out of 
the 3600 seconds in one hour, and its average speed is — 

3600 ^j_ rt^ ^ , , 

3600 - 68 ^ 1^ = 21-0 ""l V^- 

Its crest speed will be some (1*6 X 21*0 =)33-6 ml ph. If the 
train weighs 200 tons, then the engineering proposition involves 
imparting to a weight of 200 tons a speed of 33*6 ml ph, and bring- 
ing this weight to rest again every (-qT-= )106 seconds, and the 

result consists in being able to transport passengers at 17 ml ph. 
The moving-platform alternative for transporting passengers at this 
same speed, only involves a maximum speed of any moving part of 17 
ml ph. Even if there were required three other platforms, moving 
respectively at 15, 10, and 5 ml ph, these platforms need not extend 
over the entire route. Indeed, they may be confined to stations, and 
may be concentric platforms moving over an elliptical route, and 
surrounding an island platform to which the passengers gain access 
by lifts or stairs. A system of this sort might ultimately lead to 
such sound engineering solution (as the result of the study of successive 
constructions) as to ultimately result in running trains at a constant 
speed — say, 17 ml ph — and arranging for the passengers to embark 
and disembark from travelling platforms at the stations. The only 
energy required in such a system is that employed in overcoming 
friction. The enormous amount of energy required in a high-speed 
service with frequent stops, for imparting momentum to the train, 
many times per hour, would be saved. Of course, instead of platforms 
at the station, moving over an elliptical route, other arrangements 
might be adopted, such as platforms in forms resembling endless belts, 
those portions which, for the time being, constitute the upper side 
being accessible to the passengers. WhHe various types of moving 
platforms are already familiar accessories of modern life, nevertheless, 
these suggestions are not made with the serious thought of their 
early realization, but simply for the purpose of preparing the reader 
to better appreciate that the bulk of the energy consumed in train- 
propulsion is, in high-speed, frequent-stop services, required to supply 
train momentum, and with present methods, a very large part of the 
energy of momentum is ultimately wasted at the brake-shoes, as heat. 
The subject is given thorough consideration in subsequent chapters. 
For the present it may be stated that whereas a train travelling at 



INFLUENCE OF STOPS PER MILE 25 

a constant speed of 17 ml ph need not consume, at the outside, more 
than some 18 w hr per ton-mile, the maintenance of a schedule 
speed of 17 ml ph, with 2 stops per mile, would involve a consumption 
of at least 90 w hr per ton-mile, i.e, a consumption at least 5 times 
as great per ton-mile as the constant-speed proposition. 

If the total weight of the ordinary (17 ml ph) stopping- train 
is 200 tons, some 15 per cent, of this weight — or, say 30 tons — 
represents the weight of the electrical equipment, and 170 tons 
represents the weight of the trucks, under-frames, and coach bodies. 
Owing to the far lower stresses in a constant-speed train, the weight 
of the trucks, under-frames, and coach bodies would, for the same seat- 
ing capacity, be not more than, say 120 tons, and the weight of the 
electrical equipment would come down to less than 5 tons, making the 
total weight of the constant-speed train not over 125 tons. The cost 
of the two trains would be some £16,000 and £10,000 respectively. 
The £6000 saved in the capital cost per train will go far to defray the 
additional capital outlays at stations. The train consumptions will, 

90 X 200 
in the two cases, be respectively — ^-^r^:^^ — = 18*0 kelvins * per 

18 X 125 
train-mile for the stopping-train, and — — = 2*25 kelvins per 

train-mile for the constant-speed train. 

At a price at the train, of 0'8<f. per kelvin, the outlay for 
electricity for propelling the trains will be respectively — 

14:'4:d. per train-mile for the stopping-train, and 
I'Sd. „ „ „ constant-speed train. 

The electricity consumed in operating the apparatus at the stations 
would hardly be likely to exceed S'Od. per train-mile, thus leaving 
a saving on the outlay for electricity of — 

14-4 - 3-0 - 1-8 = 9'6d, per train-mile. 

I wish again to state emphatically that I am not to be understood 
as putting forward such propositions as commercial. There are 
many drawbacks, amongst which the engineering difficulties, while 
not insuperable, are certainly great. The savings in one direction 
might easily, as the result of a really thorough comparison, be much 
more than off-set by the increased outlays and operating costs in 
other directions. I have drawn attention to the future possibilities 
of such projects, with the present purpose of preparing the reader's 
mind to grasp certain important conclusions which will be dealt 
with in subsequent chapters. Two amongst these conclusions are — 
I. The preponderating influence of the momentum in problems 
relating to high-speed trains making frequent stops. 

* One kelvin equals one kw hr, i.e. 1000 w hr. 



26 ELECTRIC TRAINS 

II. Consequent upon Conclusion I. follows the second conclusion, 
namely, that for high-speed trains making frequent stops, it is of 
great commercial advantage to employ such systems of propulsion 
as shall, other things being equal, consist with low total weight of 
train for a given seating capacity. 



Examples. 

1. On a railway with an average distance of one mile between successive 
stations, the schedule speed is 24 ml ph, and the duration of stop is 10 seconds. 
From Fig. 15, find what duration of stop can be permitted in order to obtain the 
same schedule speed of 24 ml ph when the average speed is increased to 
30 ml ph. Ans. 30 seconds. 

2. An average speed of 20 ml ph and one 20-second stop per mile correspond 
to a schedule speed of 18 ml ph. Find the effect on the schedule speed of 
doubling the average speed and duration of stop. 

Ans. Schedule speed, 27*5 ml ph ; Ratio of average to schedule speed, 1*45. 

3. Passing from a suburban line with stations every 0*5 mUe, a train enters 
a section with stops every two miles. Find the possible reduction in the average 
speed if the duration of stop is constant at 30 seconds, and the schedule speed 
constant at 20 ml ph. (Use Fig. 16.) 

Ans. 30 ml ph to 21 -8 ml ph ; 27 per cent, reduction. 

4. A train is timed to traverse a 2-mile section in 5 minutes, but it has to 
make two stops at signals, of 10 seconds' and 30 seconds' duration respectivel3\ 
What is the actual average speed? Compare with the average speed for the 
normal run. 

Ans. 27*2 ml ph ; normal, 24 ml ph ; 13 per cent, increase. 

5. Find from Fig. 15 the average speeds required on a 1-mile run to give 
a schedule speed of 26 ml ph when the stops are 15, 25 and 35 seconds 
respectively. Ans. 29*5, 32-0, 35*0 ml ph. 

6. The distance between two stations is 1000 m, and has to be covered in 
2 minutes, which includes a 30-second stop. Find the schedule and average 
speeds. Ans. ]8'6; 24*9 ml ph. 

7. For 0*5, 1 and 2-mile runs determine the ratios of schedule to average speed 
for stops of 10 seconds and 30 seconds, at a constant schedule speed of 24 ml ph. 

Ans. (10 seconds) 0*975; 0*930; 0*864. (30 seconds) 0*910; 0*80; 0*60. 

8. Repeat question 7 for other schedule speeds and plot a series of curves 
for 10 and 30-second stops, and 0*5, 1 and 2-mile runs, taking schedule speeds as 
abscissae and the ratios of schedule to average speed as ordinates. There will be 
6 curves in all. 

9. From these curves ascertain the ratio of schedule to average speed for a 
1-mile run with a 30-second stop, and a schedule speed of 21 ml ph. 

Ans. 0*82. 



CHAPTER III 

TEE PREPONDERATING INFLUENCE OF MOMENTUM IN A 
SERVICE WITH FREQUENT STOPS 

For long runs with but few stops, the energy required to propel 
the train is mainly devoted to overcoming friction. But this is 
not the kind of service for which electrical operation offers much, 
if any, advantage over steam operation, except in special cases, such, 
for instance, as to do away with smoke in tunnels, and to traverse 
routes with heavy grades. The most appropriate field for railway 
electrification is at present for services of very frequent trains, 
operating at fairly high speed and with frequent stops. For this 
class of service, only a small portion of the energy employed in 
propelling the train is required to overcome friction. Most of the 
energy is employed to impart momentum to the train during the 
acceleration period, and is subsequently transformed into heat during 
the coasting and braking periods, i.e. during those periods when 
the supply of electricity has been " cut off." Thus we shall find 
that certain very important aspects of the problems involved are 
best understood by first assuming the imaginary case where the 
train has no friction other than the friction between the brake-shoes 
and the wheels. Let us further assume that the controller arrange- 
ments are such that we have " straight-line " acceleration right up 
to the crest speed. With these two assumptions, our speed-time 
diagram consists of only three sections, as shown, for a hypothetical 
case, in Fig. 18. 

In this hypothetical case, the first section occupies 24 seconds, 
and is devoted to *' straight-line " acceleration at the rate of 1 ml 
phps. Thus, at the end of 24 seconds the speed is 24 ml ph. 
The electricity is then cut off, and the train drifts. Since it is 
assumed that there is no friction prior to the application of the 
brakes, the train continues running at constant speed. This 
"drifting" section is continued for 25 seconds. At the end of 
the (24 4- 25 = )49th second from the start the brakes are applied 
at such a pressure as to decelerate the train at the rate of 1*5 ml 
phps. Consequently, since the train's speed is reduced every second 

by 1'5 ml ph the train will be brought to rest (r-^^ = )l6 seconds 

27 



28 



ELECTRIC TRAINS 



after the instant of application of the brakes. Thus, at the end of 
the (24 4-25 + 16 =)65th second from the start, the train is brought 

23 

K 

r 



^ 



^ 























r 




1 


i 








1 








\ 
















\ 






J 


1 








\ 
















) 


y 




1 












\ 





JO 20 ^40 ^o 60 70 ao 

Fig. 18. — Hypothetical Speed-time Diagram assuming no Track Friction. 

to rest. The distance traversed may be obtained as shown in 
Table VIII.— 



Table VIII. — Data obtained from the Speed-time Diagram of Fig. 18. 



Section. 


Duration 
(seconds). 


Mean speed 
(ml ph). 


Distance covered 
(miles). 


*' Straight-line " acceleration 

Drifting 

Braking ..... 


24 
25 
16 


12 
24 
12 


0080 
0-166 
0-054 


Total 


65 


— 


0-30 



A total distance of 0*30 mile is thus traversed in 65 seconds. The 
average speed for the entire run from start to stop is consequently — 

^1^ X 0-30 = 16-6 ml ph. 

65 ^ 



INFLUENCE OF MOMENTUM 29 

Taking the duration of each stop as 20 seconds, we find that the 
schedule speed is — 

65+W^16-6 = mmlph. 

During the first section of each run {ix, the section devoted to 
"straight-line" acceleration), a speed of 24 ml ph is imparted to 
the train. This is the period during which the electric motors on 
the train absorb energy from the line. Let us investigate the 
amount of energy which is stored up in the train during this period. 
In imparting to one ton a given speed S (expressed in ml ph), E, 
the energy of translational momentum expressed in w hr, which is 
absorbed by the ton, may be obtained from the formula — 

E = 0-0278 S2 * 

In our case, where the crest speed is 24 ml ph, the energy 
stored up as momentum per ton weight of train, in virtue of the 
translational motion, is consequently — 

(0-0278 X 242=)16-1 whr. 

In virtue of the momentum of the rotating parts, such, for instance, 
as the wheels and the armatures of the motors, i.e. in virtue of the 
energy of rotational motion, the total energy of momentum per ton 
weight of train will be some 9 per cent, greater than the above 
value.f 

♦ The formula may be derived as follows : — 

^ i- J. • 1 -I weight in kg , , . 
Energy of momentimi m kg m = J X — " „ X (speed m m ps)^. 

.*. For a weight of one ton (](X)0 kg), we have — 

. , 1000 , ^ . 

Energy of momentum m kg m = ^ >. 9.3]^ X (speed m m ps)-. 

But one w hr = 367 kg m 

And one ml ph = 0-447 m ps 

1000 
••• ^^^ ^ = 2^W ^ °*^^'^' ^ ^' 
. „ _ 1000 X 0-200 g2 
•• 2x9-81x367 

.-. E = 0-0278 S^ Q.E.D. 

t The energy due to the rotating parts will vary according to the design of the 
motors, wheels, etc. It vtIU generally be slightly higher for trains operated by single- 
phase motors than for trains operated by continuous motors. Wilson and Lydall, in 
" Electrical Traction," vol. i. p. 374, state that the energy due to the rotating parts 
will generally vary between 6 to 10 per cent, of the total weight of train. The subject 
is discussed at length in a paper entitled " A Consideration of the Inertia of the 
Eotating Parts of a Train," by N. W. Storer (" Transactions of the American Insti- 
tute of Electrical Engineers," vol. xix. p. 165). Garter, in his contribution to a 
discussion on " Electric Railways," at the Institution of Civil Engineers (" Proceed- 
ings, Institution of Civil Engineers," vol. clxxix. pt. 1), gives the following method 



30 ELECTRIC TRAINS 

Thus, the total energy of momentum of the train, when it is 
running at a speed of 24 ml ph, is — 

(1-09 X 16-1 =)17-5 w hr per ton, 
or 17-5 X 3600 = 63,000 w sec per ton. 

Since this amount of energy is absorbed by the train during the 24 
seconds occupied in accelerating the train, the rate at which the 
energy is being stored up as momentum by the train, averaged over 
the entire accelerating period, is — 

63,000 w sec „„^^ ,, « ^^ , 

-^T 3— = ^o JO watts per ton ; or 2*62 kw per ton. 

But the average rate at which energy is being stored up in the train 
as momentum, when spread over the 65 seconds during which the train 
is in motion, is — 

63,000 w sec „^,_ ,, , ^ r^^ -, 

— — J — = 970 watts per ton : or 0'97 kw per ton. 

65 seconds ^ ' ^ 

Including a 20-second stop at each station, the average rate at which 
energy is being stored up in the train as momentum, taken over the 
whole route, is — 

65 
^p. ^^ X 970 = 740 watts per ton ; or 0*74 kw per ton. 

Thus we have — 
Energy absorbed, per ton, in momentum — 

(a) Averaged over the time during which the train 

is taking electricity from the line . . .2*62 kw. 

(b) Averaged over the time during which the train 

is in motion ....... 0*97 kw. 

(c) Averaged over the entire route . . . . 0*74 kw. 

If the train in question has a total weight of 100 tons, the 
average rate at which energy is stored up in the train as momentum, 
taken over the whole route, is — 

100 X 0-74 = 74 kw. 

— _ g 

of allowing for rotational momentum when there is no special knowledge of the 
moments of inertia of the respective train parts. 

Add to the weight of the train an amount equal to — 

[(0-6 xw)+0-5xax(^^x gyi 

where w = weight of all train wheels, 

a = weight of all armatures, 

d = outer diameter of armature, 

D = diameter of driving wheel, 

g = gear ratio. 
The total momentum energy (including rotational) can then be estimated simply as 
energy for linear momentum on the above estimated total weight. 



INFLUENCE OF MOMENTUM 



31 



In the case of a road operating 100 such trains simultaneously, 
from a single power-house, the peaks of load will be so distributed 
that the rate at which energy is being stored up as momentum in 
these 100 trains will be fairly uniform at — 

100 X 74 = 7400 kw. 

Modification of the Results as reg^ards Con= 
sumption per Train when Friction is taken 
into Consideration 

When friction is considered, the drifting portion of the speed- 
time diagram will no longer be a horizontal line representing 
constant speed, but the line will slope so as to represent a drift- 
deceleration of 0'07 ml phps. 

This change has been made in Fig. 19, where it is seen that the 

28 
24 
'%20 

^^ 



-f^^' ■ ■•i^^ 



/O 20 30 >^ 50 60 JO dO 
77me /n Seconds 

Fig. 19. — Hypothetical Speed-time Diagram taking Track Friction into Account. 



distance covered can be maintained at the same value by raising the 
crest speed, and lowering the speed at which braking commences, 
thus keeping the same area enclosed by the speed-time diagram.* 

♦ It has already been explained, on p. 15 of Chapter I., that the distance traversed 
is equal to the area of the speed-time diagram. 



32 ELECTRIC TRAINS 

These changes would, however, make only slight differences in the 
energy considerations which follow, and it is not worth while taking 
them into account, since the conditions of this schedule are purely 
hypothetical, and are intended only to assist in describing useful 
ideas and methods of carrying out train-movement calculations. 

The energy stored up in the train as momentum is subsequently 
transformed by friction into heat. This friction occurs at the bear- 
ings of the rotating parts, at the points of contact of wheel and track, 
at the ends and sides of the train, and, chiefly, at the brake-shoes. 

It was asserted at the commencement of this chapter that, when 
trains are operated at high schedule speed and with frequent stops, 
much the greater part of the energy consumed at the train is required 
for providing the momentum corresponding to the maximum speed of 
the train, and that the energy required for overcoming train-friction 
is, in comparison, only a small amount. Let us now examine the 
correctness of this assertion. 

The quantity of energy transformed into heat at the bearings of 
the rotating parts, and at the points of contact of wheel and track, 
may be considered to be inevitably associated with the propulsion of 
the train, and the quantity of energy consequently is, in a sense, 
effectively employed. The energy transformed into heat at the 
brake-shoes may, on the other hand, be regarded as wasted. 

If the rolling stock is of good design, then, when the train is 
operated at constant speed, on a straight, level, and well-built per- 
manent way, the tractive force required per ton > weight of train 
may, for a train of 100 tons weight, be taken at the values set forth 
in Table IX.— 

Table IX. — Teactive Foece eequieed at Axles to overcome Teain 
Resistance at Vaeious Speeds. 



Speed (ml ph). 


Tractive force required to overcome 
train resistance (kg per ton). 


10 


1-5 


20 


2-6 


30 


3-6 


40 


4-7 


50 


6-6 


60 


8-3 


80 


12-8 


100 


18-6 



There are 1609 m in one mile.* Furthermore, 367 kg m equal 



* One mile = 1609*3 m. ^ The figure may be taken as 1609 or 1610, according to 
the degree of accuracy required, i.e. according as the calculation justifies 4 or only 
3 significant figures. 



INFLUENCE OF MOMENTUM 



33 



1 w hr. From these two constants, and the data in the preceding 
table, we may compile the results in Table X. — 

Table X. — Energy required at Axles to overcome Train Friction 

AT Various Speeds. 





Energy required at 


Energy required at 


Speed (nil ph). 


axles to overcome train- 


axles to overcome train- 


friction (kg m per 


friction (w hr per 




ton-mfle). 


ton mile). 


10 


2,410 


7 


20 


3,700 


10 


30 


5,800 


16 


40 


7,550 


21 


50 


10,600 


29 


60 


13,300 


36 


80 


20,600 


56 


100 


29,800 


81 



These are rough estimates of the amounts of energy which would 
be required at the axles to overcome friction in propelling well- 
built trains at constant speed over a well-built, straight, and level 
track. 

But when the speed of a train is rapidly changing throughout the 
journey, as in the case of a service with frequent stops, these train- 
friction data are found not to apply in practice. The train-friction 
is considerably higher than would be inferred from these data 
when taken to correspond to the mean speed of the train. We shall 
introduce no serious error into the results obtained in estimating the 
total energy consumed at the train, if we take the train-friction 
at a liberally high value. In fact, we are justified in simplifying the 
calculations by taking the tractive force per ton as of a constant 
value throughout the journey. A convenient and safe value to 
assume for the tractive force, for trains operating with frequent 
stops and with a crest speed of not over some 45 ml ph, is 6 kg per 
ton, even though the mean or average speed may be only some 15 to 
30 ml ph. We thus see that the tractive force is taken at fully 
twice the value shown in the table, for a constant speed equal to the 
mean speed. In our example, namely, that of a 100-ton train 
running to a schedule speed of 12*7 ml ph, and with a stop every 
0'30 mile, we may calculate the energy required at the axles as 
follows : — 



Tractive force 
Train-friction 



6 kg per ton. 

6 X 1609 = 9650 kg m per ton-mile 

^ = 26*2 w hr per ton-mile. 



D 



34 ELECTRIC TRAINS 

We have seen in Table VIII. that the distance covered during the 
time that the train is taking electricity from the line, i.e. during the 
24 seconds occupied by acceleration, is 0*080 mile. Consequently, 
the electricity required to overcome the train-friction during the first 
24 seconds is — 

26-2 X 0-080 = 210 w hr per ton. 

During the remaining 41 seconds of the run from start to stop, the 
electricity is cut off from the train, and the momentum of the train 
is drawn upon as the source of power to overcome train-friction 
during the remainder of the journey. During the 20-second stop 
at the station, there is, of course, no train-friction. Thus, every 
(24 -h 41 -f- 20 =)85 seconds, 2*10 w hr are taken from the line by 
the train, to overcome train-friction, and in the course of one hour 
the total amount of electricity consumed in overcoming train- friction 
is — 

-^:r=~ X 2*10 = 89 w hr per ton. 

85 

The energy consumption in w hr per hour may, of course, be 
expressed in terms of power, i.e. of the rate of consumption of energy. 
Thus— 

1 w hr per hour = 1 watt. 

We consequently arrive at the result that the average rate of con- 
sumption of electricity for overcoming the friction of the train is, 
taken over the entire route — 

89 watts per ton. 

We have seen (on p. 30) that, taken over the entire route, the 
average rate of consumption of energy for the purpose of providing 
momentum is — 

740 watts per ton. 

Thus, still retaining our assumption of 100 per cent, efficiency of the 
electrical equipment, we find that the average rate of consumption of 
electricity by the train is — 

740 + 89 = 829 watts per ton. 

Determination of the Amount of Ener§:y wasted 
as Heat at the Brakes 

During drifting, and braking the train covers, as we find from 
Table VIII., on p. 28— 

0166 -h 0-054 = 0-22 mile. 

The energy required to overcome friction over this distance is — 

26-2 X 0-22 = 5-8 w hr per ton. 



INFLUENCE OF MOMENTUM 35 

Thus every 85 seconds, the energy of momentum is drawn upon 
to the extent of 5*8 w hr per ton to overcome train-friction, and in 
the course of one hour the total amount of momentum employed in 
overcoming train-friction is — 

— — X 5*8 = 250 w hr per ton. 

Consequently, the average rate, taken over the whole route, at which 
train-friction is being provided from the train's momentum is 250 
watts per ton. We have already seen that the average rate at which 
energy is being accumulated in the form of momentum is — 

740 watts per ton. 

Other than in overcoming train-friction, the momentum is ultimately 
transformed into heat at the brake-shoes. The rate, taken over the 
entire route, at which energy is being transformed into heat at the 
brake-shoes is — 

740 - 250 = 490 watts per ton. 

Thus, in the present case, the energy ultimately wasted as heat at 
the brake-shoes constitutes — 



490 

f^jY] X 100 = 66*3 per cent. 



of the energy present in the train as momentum at the instant of 
attaining crest speed. 

The average value of the power employed for train-friction, taken 
over the entire route, and including that taken directly from the line 
and that drawn from the momentum, is equal to — 

829 - 490 = 339 watts per ton. 

Obviously, the same result is arrived at by adding 89 watts per ton, 
the average of the amount taken directly from the line as electricity, 
and 250 watts per ton, the amount taken from the stored- up energy 
of motion (ix, the momentum) of the train. Thus we have also — 

89 + 250 = 339 watts per ton. 

Modification of Calculations to take into Account 
the Losses in the Electrical Equipment on 
the Train 

The train requires per ton an input from the line, at an average 
rate equal to 829 watts, plus the losses in the electrical equipment. 
For such a case as that which we are considering, we may (with 
sufficient accuracy, at any rate, for the purposes of this example) take 
the over-all efficiency of the electrical equipment on the train, averaged 



36 



ELECTRIC TRAINS 



over the whole route (i.e. including stops) at 72 per cent. Conse- 
quently, the average input to the train is — 

^r^ = 1150 watts per ton. 

1150 watts per ton is, of course, 1150 w hr per ton per hour. Since 
the train covers 12*7 miles in one hour, the average rate of input 
of energy to the train may also be expressed as — 

Yo7>f — ^^'^ ^ ^^ P®^ ton-mile. 

We have seen that the average rate at which energy is being trans- 
formed into momentum is 740 watts per ton. This is — 

740 

ry^ X 100 = 64-3 per cent. 

of the total input from the line to the train. 

The average rate at which energy is devoted to the purposes of 
actual propulsion is — 

,^X 100 = 29-5 per cent. 
1150 ^ 

of the total input from the line to the train. 

Thus, we may say that, for this schedule, the "propulsive efficiency " 
is 29'5 per cent. By this we mean that, could we eliminate the losses 
in the electrical equipment and at the brake-shoes, only 29*5 per cent, 
as much energy would be required to operate the train as is, owing 
to these losses, actually required. 

We can summarize these results as indicated in Table XI. — 

Table XI. — Allocation op Power consumed by a Tbain during a Given Run. 





Average power 
required (watts). 


Ditto, in per cent., 

of total power 

required. 


Average rate at which energy is transformed into 
heat at the brake-shoes, per ton weight of train 

Ditto into heat associated with useful propulsion, 
per ton weight of train ..... 

Ditto into heat in the electrical equipment, per 
ton weight of train (1150 - 490 - 339 =) . 


490 
339 
321 


42-6 
29-5 
27-9 


Total input to train per ton of weight . 


1150 


100 



From these results we find ample justification for the statement 
that, for the more usual and appropriate cases of railway electrifica- 
tion, a leading occurrence relates to imparting momentum to the 
train, and subsequently transforming this momentum into heat at 



INFLUENCE OF MOMENTUM 



37 



the brake-shoes. In the example we have taken, the average power 
consumption of the train is 1150 watts per ton. If we had assumed 
zero train-friction, still taking the average efficiency of the electrical 
equipment as 72 per cent., the average power consumption of the 
train for the entire run would have been — 

740 

^r-=7i = 1030 watts per ton. 

0*72 ^ 

If, furthermore, we had assumed 100 per cent, efficiency of the 
electrical equipment, then the average power consumption of the 
train, taken over the entire run, would have been — 

740 

— — = 740 watts per ton. 

Ke verting again from *' average power consumption " to " energy 
consumption per ton-mile,'* we have the following results for the 
example we have taken — 

{a) Energy consumed by the train on the assumption of a train- 
friction of 6 kg per ton = 90*5 w hr per ton-mile. 

(6) Ditto, on the assumption of 100 per cent, efficiency of electrical 
equipment 

72 
= ZTTT?: X 90*5 = 79*6 w hr per ton-mile. 

(c) Ditto, on the further assumption of zero train-friction — 

0-0278 X 1-09 X 242 ^^ , . 

^r;^^ = 58*1 w hr per ton-mile. 

The readily-obtained values set forth in Table XII. are also of 
interest — 



Table XII. — Allocation of Energy consumed by a Train during a 

Given Run. 



Ultimate allocation of the energy. 


W hr per tou- 
mile. 


Per cent, of total 
input. 


Energy transformed into heat at the brake-shoes 
f^90_\ 

Ditto into heat associated with useful propulsion, 
i.e. into train-friction i — - = j 

Ditto into heat in the electrical equipment ( -^ = 1 


38-6 

26'7 
25-2 


42-6 

29-5 
27-9 


Total 


90-5 


100 



38 



ELECTRIC TRAINS 



The energy present as momentum at the instant of attaining crest 

speed is 58'1 w hr per ton -mile, which is (qtttk ^ 1^0 = j64*3 per 

cent, of the input to the train. This last value, and the three values 
in Table XII., are represented graphically in Fig. 20. 




Fig. 20. — Diagram showing the Allocation of the Energy Input for a Service 
with an Average Distance of 0*30 Mile from Start to Stop, and a Schedule 
Speed of 12-7 ml ph (see Table XII., on p. 37). 

In considering the case of zero train-friction and 100 per cent, 
efficiency of the electrical equipment, the energy distribution is as 
follows : — 

Input to train = Momentum energy = Brake waste. 

Allowing for losses in the electrical equipment, but retaining the 
assumption of zero train-friction, the distribution becomes — 



INFLUENCE OF MOMENTUM 39 

-Heat loss in electrical equipment — 



Input to train- 



-Momentum energy (= Brake waste) — 



If 100 per cent, efficiency of the electrical equipment is again 
assumed, but allowance is made for train-friction, then the distribution 
is shown by — 



— ^Brake waste- 
S — Momentum energy — 

f3 3 — 
pj ^ 



/Train-friction energy\ ,m j. 1 i. • r.- j.- ^ 

~i after cut-off M Total tram-friction 

' — < energy used in>- 

— Train-friction energy up to cut-off ' I propulsion ) 

Finally, we have the general case of actual practice — 

— Heat loss in the electrical equipment — 

I — Brake waste 



e3 
•43 







— Momentum energy- 



I /Train-friction energy \ ,m 4. 1 j. • x • j.- , 

-\ after cut-off /-| Total tram-friction 

^ ' — < energy used in> — 

-Train-friction energy up to cut-off ' I Propulsion ) 



Calculations similar to the example in this chapter have been 
carried out for runs of 0*5, 1, 2, and 4 miles at schedule speeds of 15, 
20, 25, and 30 ml ph. The results obtained are embodied in the 
curves of Figs. 21, 22, 23 and 24, which show, for these schedules, 
how the total input is distributed. 

Fig. 25 is diagrammatic, and brings out the great contrast in the 
allocation of the energy for widely differing schedules. 

When comparison is made with the results of practical tests, 
variations will, of course, be found in all cases, since it is impossible 
to estimate with complete precision the energy input for a given case; 
it varies greatly with profile of the track, the conditions of rail service, 
the design of the rolling stock, the type of equipment, the methods of 
motor control, and even the qualifications of the driver. The subject 
has been discussed from the standpoint employed in this chapter for 
the purpose of logically paving the way for the more useful (although 
somewhat less obvious) methods which will be set forth in the imme- 
diately following chapters. 

In examining Figs. 21 to 25 special attention should be given 
to the influence of the schedule speed and the distance between stops. 
For a given schedule speed, then, the greater the distance between 
stops, the less is the percentage of energy wasted at the brakes, and 




pi 

P4 1 



e3 

o 

EH 



bO 

e3 

o 
o 



03 
O 



Qusju^ 



pq 



OS 
(S 

w 



03 
I 




bo 
eS 

® 
o 

<D 

PM 
m 
c3 

o 
o 

P4 



GQ 






1^ 



<pU9QU^ 




ju3<)uy 



42 



ELECTRIC TRAINS 



the greater is the percentage which may be considered as propulsion 
energy. Conversely, with a given distance between stops, the pro- 
pulsion energy is a greater percentage of the total input, the lower 
the schedule speed. Fig. 23 shows rather strikingly the relatively 



Schedu/e S/ieeci - /5 m/ph 



D'siance hetirStcffs 'Jmik Di's^noc iet/^Sbobs=4m<Te'. 



Cneryif 








Schedtt/e S/xecf-30m//3?i. 



Distance batrf. Stops 'J/ri/e 



■;.\-' Clec.fjimo. .'•■■■' 







D/itunce beJK Sites' 4m/e« 







Fig. 25. — Diagrams showing Allotment of Total Input to 100-ton Train for DiHerent 
Services, taken from the Curves of Figs. 21 to 24, and representing Actual Kuns. 

small percentages of the energy which is wasted in the electrical 
equipment, and the comparative independence of this percentage on 
the schedule speed, and even on the distance between stops. 



Examples. 

1. What is the amount of energy contained in a 50- ton train running at a speed 
of 20 ml ph (including the energy due to rotating parts, which may be taken as 9 
per cent.) ? Ans. 605 w hr. 

2. Neglecting track friction, what amount of energy must be expended to accele- 
rate a 75-ton train from 25 ml ph to 40 ml ph ? Ans. 2*22 kw hr. 

3. 1 w hr = 367 kg m. What distance would a train run on straight level 
track against track friction (of 3 kg per ton) by virtue of its energy of momentum at 
15 ml ph ? ^ Ans. 832 m. 

4. A train running at 30 ml ph mounts an incline of 1 in 100. How far will it 
run up the incline before its momentum energy is consumed, neglecting track friction? 

Ans. 1000 m. 

5. What would have been the distance run in question 4 if the track friction 
were 4 kg per ton ? Ans. 715 m. 

6. A train weighing 150 tons and travelling at 51 ml ph is brought to rest in 
30 seconds. Assuming no track friction, determine: {a) The decelerating rate. 



INFLUENCE OF MOMENTUM 43 

(b) The energy wasted at the brake-shoes in kw hr. (c) The average rate at which 
energy, expressed in watts per ton weight of train, is being wasted at the brake- 
shoes. -4ns. (a) 1'7 ml phps. 

(&) 11-8 kw hr. 

(c) 9450 watts per ton. 

7. A train absorbed energy at the axles at the average rate of 300 kw for 40 
seconds, and accelerated during this time at 1*2 ml phps. Assuming no friction, 
determine the weight of the train. Ans. 48 tons. 

8. From Table IX., (a) What would be the tractive force of a locomotive hauhng 
a train of five 20-ton coaches at a constant speed of 40 ml ph on straight, level 
track, and (b) How much energy is needed to propel the coaches over a distance of 4 
miles ? 

Ans. (a) 4700 kg. 
(&) 8-2 kw hr. 

9. A hypothetical train is accelerated at a steady rate of 1*0 ml phps up to a 
crest speed of 50 ml ph, and the train-friction averages 6 kg per ton. Find the 
components of (a) the energy input for friction, and (b) the energy input for 
momentum. Ans. (a) Friction — 9'1 w hr per ton. 

(&) Momentum — 75'9 w hr per ton. 

10. (a) What is the distance covered up to crest speed in question 9 ? (6) Compare 
the energy input during the accelerating period in question 9 with the input neces- 
sary to propel the train the same distance at the constant speed of 50 ml ph (see 
Table XX.). Ans. (a) Distance — 558 m. 

(&) Accelerating period — 85 w hr per ton. 
Constant speed — 10 w hr per ton. 

11. The average rate of input to twenty 100-ton trains operating to a schedule 
speed of 20 ml ph is 2000 kw. Find the average input to the trains in w hr per 
ton-mile. Ans. 50 w hr per ton-mile. 

12. If the propulsive efficiency is 30 per cent, in question 11, find the average 
input for overcoming friction. Ans. 300 watts per ton. 

13. A three-coach train weighing 100 tons has a total of 12 axles and 24 wheels, 
each wheel being 1000 mm diameter and weighing 250 kg. The train is driven by 
4 motors, each of the armatures of which weigh 1200 kg and measure 400 mm in 
diameter. If the gear ratio is 3*7, find the weight which must be added to the 
weight of train to allow for the rotational inertia of the armatures and wheels. 
Employ Carter's formula in footnote of page 30. Express the weight as a per- 
centage of the total train weight. Ans. 8*9 per cent. 



CHAPTER lY 

A METHOD OF ESTIMATING TEE ENERGY CONSUMPTION OF 
TRAINS, ON THE ASSUMPTION OF NEGLIGIBLE TRAIN- 
FRICTION AND OF ONE HUNDRED PER CENT. EFFI- 
CIENCY OF THE ELECTRICAL EQUIPMENT ON THE 
TRAIN 

The investigations in the preceding chapter have shown that when 
trains are operated at high schedule speeds, and with frequent stops, a 
large percentage of the total energy consumed by the train is required 
in providing the momentum corresponding to the crest speed (i.e. the 
maximum speed attained at any time during the run), and that a large 
part of this energy of momentum is subsequently transformed into 
heat at the brake-shoes. 

In order to bring clearly into prominence the significance of this 
circumstance as affecting the question of the electric operation of city 
and suburban railways, it is very instructive to consider, in the first 
instance, the case of a train assumed to have no friction loss (other 
than at the brake-shoes), and no loss in the electrical equipment. 
Thus, the only energy consumed by the train is that transformed 
into the momentum of the train corresponding to its crest speed. 

Let us first work out several cases where the acceleration from 
rest, up to the crest speed, is of the uniform value of 1 ml phps. 
When the crest speed is reached, the supply of electricity is cut off, 
and the train runs at constant speed (since we have assumed that 
there is no train-friction) until the brakes are applied. The brake 
pressure is assumed to be adjusted at such a value that the deceleration 
is 1*5 ml phps. The shape of the speed-time diagram corresponding 
to these conditions is shown in Fig. 26. With these rates of acceleration 
and deceleration, let us first work through a case where the schedule 
speed is 18 ml ph, and where the train makes one 20-second stop 
per mile. 

In one hour there will be 18 stops. Therefore, the total time 
during which the train is at rest during each hour is equal to — 

18 X 20 = 360 seconds. 

44 



ENERGY CONSUMPTION 45 

Consequently, the train is in motion for — 

3600 - 360 = 3240 seconds per hour, 
and the time occupied by one run from start to stop is equal to — 

3240 



18 



= 180 seconds. 



Let us denote by F the crest speed (i.e. the maximum speed attained 
by the train at any time during the run) in ml ph. Then the 



























mlbl 


fon 






I 






on 






t 


/ 








<( 


/ / 




^ 
5 






/ 








\ 






^ 

^ 
tt\ 




1 










\ 






^^ 




/ 












\ 






/ 














\ 






/ 














\ 





Pig. 26. — Hypothetical Speed-time Diagram, with Acceleration and Deceleration of 
I'O and 1*5 ml phps respectively, and no Track Friction. • 

number of seconds occupied in accelerating the train at 1*0 ml phps 
is equal to — 

F 



1-0 



= F 



Since the deceleration is at 1*5 ml phps as against an accelera- 
tion of I'O ml phps the number of seconds during which the train 
is being braked is equal to 

1-5 

The number of seconds during which the train is running at constant 
speed is equal to — ^ 

180 - F - r-g. 

I'O 



46 



ELECTRIC TRAINS 



We thus have the values in Table XIII. — 

Table XIII. — Showing the Dueation of, and the Avebage Speed and 
Distance covebed dueing, the AccEiiEEATiNG, Constant Speed and 
Deceleeating Peeiods op the Speed-time Diagbam of Fig. 26, when taken 
to ebpeesent a i-MiLE EuN at a Schedule Speed of 18 ml ph. 



— 


Duration 
(seconds). 


Duration (hours). 


Average 

speed 
(ml ph). 


Distance covered 
(miles). 


Accelerating | 
period / 

Constant speed j 
period / 

Decelerating \ 
period j 


F 

F 
180-F-f^ 
1*5 

F 

1-5 


xF 
3600^ 

1 F 
3600^1-5 


F 
2 

F 

F 

2 


1 -n, F 
xFx 
3600 2 

IFF 
3600^1-5^2 



The total distance traversed is one mile ; therefore, by adding the 
distances covered during the three periods, we have — 



1 /F^ 5 „ Y^\ 



3600 



3600\2 



^F2- 180r= -3600 
b 



r2 - 216F = -4330 

ya _ 216F + 11,670 = -4330 + 11,670 

F - 108 = f85-7 

F = 22-3 

/. The crest speed is equal to 22'3 ml ph. 

22*3 
Duration of accelerating period = -j^ = 22*3 seconds. 

Duration of constant speed period 

22-3 



= 180 - 22-3 - 



1-5 
22-3 



= 142*8 seconds. 



Duration of braking period = -^^ = 14*9 seconds. 

Since we have assumed that the friction is negligible, we have only 
to consider the energy required to give the necessary momentum at 
this crest speed. 

Energy of translational momentum per ton is equal to — 

0-0278 X (22-3)2 = 13-8 w hr. 



ENERGY CONSUMPTION 



47 



The energy of rotational momentum of the revolving parts, con- 
sisting of the wheels of the trucks and the armatures of the motors, 
will, in most cases, increase the above amount by some 9 per cent. 
Consequently, we have — 

Energy of translational and rotational momentum per ton is 
equal to — 

1-09 X 0-0278 X (22-3)2 
= 0-0303 X (22-3)2 
= 15-0 w hr. 

We have carried out, step by step, the calculations for this first 
case. It will now, however, be of interest to develop a formula by 
means of which the calculations of such cases may be considerably 
expedited. Let us, as before, denote the crest speed by F. 

Let A equal the acceleration in ml phps. 
„ B „ „ deceleration during braking in ml phps. 
„ T „ „ time in seconds occupied by a single run from start 

to stop. 
„ M „ „ distance in miles from start to stop. 
„ F „ „ crest speed in ml ph. 

We first obtain the values in Table XIV. — 

Table XIV. — Showing the Dueation of, and the Aveeage Speed and 
Distance coveeed dueing, the Acceleeating, Constant Speed and 
Deceleeating Peeiods of a Repeesentative Speed-time Diageam. 



Accelerating period 
Constant speed period . 
Decelerating period . 



Duration 
(seconds). 



F 
A 

A B 

F 

B 



Duration (hours). 



1 F 
3600^ A 

3600\-^ A B/ 
1 F 
3600^B 



Average 

speed 
(ml ph). 



F 
2 

F 

F 
2 



Distance covered 
(mile). 



1 F F 
3600^ A^ 2 

>00V A B/ 



3600 



F 



1 F F 
3600^B^ 2 



Total distance covered in miles is equal to M. 



)00V2A ^ A "" B "^ 2B/ ~ 



M 



F2 F^ 

2A + 2B-T^=-^X^^^^ 



A + B 
2AB 



X F2 - TF = - M X 3600 



48 



and F = 



ELECTRIC TRAINS 



Let 



AB 



= C 



A + B 

/. F2 - 2C X T X F = -7200 x C x M 
20 X T + 2\/C2 X T2 - 7200 x C x M 



Thus, for F, the Crest Speed, we have the formula — 
F = C X T - VC2 X T^ - 7200 x C X M 

since the positive value before the root will be always inadmissible. 
Values of C are found (for any particular acceleration and decele- 
ration) from Table XV. — 



Table XV.— 


■Values of C 


FOB Vabious Accelebations and Decelebations. 


o-^ 


The factor C, in the crest-speed formula, for the following values of B, the braking deceleration 


, the 
erat 
php 


(ml phps). 




B=l-0. 


8=1-1. 


8=1 "2. 


1 

8=1-3. 


8=1-4. 


8=1-5. 


8=1-6. 


8=1-7. 


8=1-8. 


8=1'9. 


8=2-0. 


0-5 


0-333 


0-844 


0-363 


0-361 


0-368 


0-375 


0-381 


0-386 


0-391 


0-396 


0-40 


0-6 


0-375 


0-388 


0-40 


0-411 


0-420 


0-429 


0-436 


0-443 


0-450 


0-466 


0-462 


0-7 


0-412 


0-428 


0-442 


0-455 


0-467 


0-478 


0-487 


0-496 


0-504 


0-512 


0-519 


0-8 


0-444 


0-463 


0-480 


0-495 


0-509 


0-622 


0-633 


0-644 


0-554 


0-563 


0-571 


0-9 


0-474 


0-495 


0-514 


0-532 


0-648 


0-563 


0-676 


0-588 


0-60 


0-611 


0-621 


1-0 


0-50 


0-524 


0-546 


0-565 


0-683 


0-60 


0-615 


0-630 


0-643 


0-666 


0-667 


1-1 


0-624 


0-650 


0-574 


0-596 


0-616 


0-634 


0-652 


0-668 


0-683 


0-697 


0-710 


1-2 


0-645 


0-574 


0-60 


0-624 


0-646 


0-667 


0-686 


0-703 


0-720 


0-785 


0-750 


1-3 


0-665 


0-696 


0-624 


0-650 


0-674 


0-696 


0-717 


0-737 


0-755 


0-772 


0-788 


1-4 


0-583 


0-616 


0-646 


0-674 


0-70 


0-724 


0-747 


0-768 


0-787 


0-806 


0-824 


1-5 


0-60 


0-635 


0-667 


0-696 


0-724 


0-750 


0-774 


0-797 


0-818 


0-838 


0-857 


1-6 


0-615 


0-652 


0-686 


0-717 


0-747 


0-774 


0-80 


0-824 


0-847 


0-869 


0-889 


1-7 


0-630 


0-668 


0-703 


0-737 


0-768 


0-797 


0-824 


0-850 


0-874 


0-897 


0-919 


1-8 


0-643 


0-683 


0-720 


0-765 


0-787 


0-818 


0-847 


0-874 


0-90 


0-924 


0-947 


1-9 


0-655 


0-697 


0-735 


0-772 


0-806 


0-838 


0-869 


0-897 


0-924 


0-960 


0-974 


2-0 


0-667 


0-710 


0-750 


0-788 


0-824 


0-857 


0-889 


0-919 


0-947 


0-974 


1-00 



By means of the above formula for the crest speed, and of 
Table XV., we can quickly carry through calculations, on the 
assumptions employed in this chapter, for the energy consumed at 
the train per ton-mile. 

Let us first take the case of a route where the distance between 
stations is 0*5 mile. Let the acceleration be 1*0 ml phps and the 
deceleration during braking 1'5 ml phps, i.e. — 

M = 0-5 A = 1-0 B = 1-5. 
For these conditions let us estimate the consumption in watt-hours 
per ton-mile for speeds of 9, 12, 15 and 18 ml ph. Let the duration 
of each stop be 20 seconds in all cases, i.e. let Q = 20. 



ENERGY CONSUMPTION 



49 



We may carry out the calculations in orderly form, as in the first 
part of Table XVI., which also shows similar calculations for 1-, 2- 
and 4-mile runs with the same acceleration and deceleration. 
Considering the results for a 0*5 -mile run, in doubling the schedule 
speed (from 9 ml ph to 18 ml ph) we have considerably more than 
trebled the crest speed ; and the values in the last horizontal line of 
these calculations show that for the higher schedule speed (18 ml 
ph) the value of the w hr per ton-mile is eleven times as great as 
for the lower schedule speed (9 ml ph). 

In Fig. 27 are plotted, for various values of M (the distance in 




/O 20 30 

Schec^u/e 3pecc( m/ ph 



JO 



Fig. 27. — Eatio of Crest to Schedule Speed for Various Schedule Speeds and Runs ; 
with Acceleration of 1-0 ml phps, Braking 1*5 ml phps. (Neglecting Decelera- 
tion during Coasting, i.e. assuming Frictionless Run.) 



miles from start to stop), the corr.esponding ratios of the crest speed 
to the schedule speed. 

The shape of the curves indicates the limiting values for the 
attainable speeds for these values of the acceleration and deceleration. 
Thus, it is evident that with a distance of only 0*5 mile from start to 
stop, and with these values of the acceleration and deceleration, a 

E 



o 
o 



H !^ 

H M 

^ e8 

O ^ 

QQ 'H 

O ® 



o 

d 



§ H 



P4 



X II 
O r^ 

O Q 



O 



M CM 
K> ^ 



O 



O 
CO 
(N 



o 
1— i 



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o o 

(M 00 

Tt* CO 



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uo «o 

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<M <>J 

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c<r 

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o 

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o 

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CO 

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00"* 
CO (N 

CO 


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(M 

CO 


132 1 90 78 
17,420 8,100 6,084 


168 
28,220 



oo 



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oa 




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Tt< 


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t* 




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iH 


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L-^ 


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T-t 


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o y^ 

1-1 Ttl 

of Zl 






o 



o 


o 


o 


o 


o 


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CO" 


rH 


o 


o 


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CN 


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■^ 


co" 


1— ( 



00 -* 

Tj< O 
CO 



00 "^ 
t> 00 

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s <? 





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r-T 


o 

CN 




i-( 


(M V' 

3S <M 

co-^^ 


CO 
1—1 


00 
(N 


rH 



a 



.2 

n 



(X 







CJ OJ 



a 



.2 o 

ft 



Ci {5CS O 

o) ja 2 a> 

O 3 03 

S o*2 S 

1— 4 o a) f— ( 

H H 



• -I-' 02 

'^ aj °^ O 
S fl o ■« 



O 



O 



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H 
H Q 

o> 



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(M o 



02 I ^ 

(-1 cf 



■^'^ 

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<u S <» 

s S s 1=^ 



ENERGY CONSUMPTION 



51 



schedule speed of 20 ml ph is unattainable, as also a speed of 
30 ml ph for M = 1-0. 

In Fig. 28 are shown curves, drawn for various values of M, 
with schedule speeds as abscissae and with the energy consumption 
in w hr per ton-mile as ordinates. 

This last figure shows us that the energy consumption (for fric- 
tionless runs and 100 per cent, efficiency of equipment) increases 




/O 20 30 ^ 

3ohedu/e S/oeecf ^n m/ ph 



^O 



Fig. 28. — Energy Consumption for Various Schedule Speeds and Runs under the 
assumed Frictionless Conditions, and 100 per cent. Efficiency of Electrical 
Equipment. Acceleration I'D ml phps ; Braking 1*5 ml phps. 



at an exceedingly rapid rate (as the square, in fact, of the crest 
speed). From Fig. 27 we have already seen that the crest speed 
increases much more rapidly than the schedule speed. For these 
reasons, schedule speeds are soon reached which, while attainable, 
are not commercial, as the cost of the required energy would be 
prohibitive. The limiting schedule speed, when commercial con- 
siderations are taken into account, is, for short distances between 
stops, very much lower than is generally appreciated. In Table 
XVII. are given values of the schedule speeds attainable with various 



52 



ELECTRIC TRAINS 



values of the energy input for supplying momentum, for runs of 0*5, 
I'O, and 2*0 miles from start to stop, the values being taken from 

Fig. 28. 

Table XVII. — Schedule Speeds attainable with Various Values of Energy 
Input, and with Different Lengths of Run, assuming Friotionlbss Runs 

and 100 PER CENT. EFFICIENCY OF ELECTRICAL EQUIPMENT. 



Distance from start to 


Schedule speed in ml ph for the following values of the energy input to 
provide momentum (w hr per ton-mile). 


stop (miles). 


40 w hr per ton-mile. 


50 w hr per ton-mile. 


60 w hr per Ion-mile. 


0-5 
1-0 
2-0 


16-4 
23-7 
35"2 


16-9 
25-0 
37-3 


17-3 

25-7 
38-5 



It must be distinctly remembered that the above values only 
apply to the values of the acceleration and deceleration (A = I'O and 
B = 1'5) employed in the calculations, and are also restricted to 
the assumptions made throughout this chapter, namely, that the 
train-friction is negligible and that the efficiency of the electrical 
equipment is 100 per cent. 



The Influence of the Values of the Acceleration 
and Deceleration on the Energy Consumption 
at the Train 

Let us take the case of a 0'5-mile run from start to stop. Thus, 
M = 0*5, Let the acceleration and deceleration be infinite, and let 
the train run at a constant speed of 20 ml ph from start to stop. 
Then the time occupied in covering the 0*5-mile distance from start 
to stop will be — 

^ X 3600 = 90 seconds. 

Taking the duration of the stop as 20 seconds, the schedule speed is — 

90 



110 



X 20 = 16-3 ml ph. 



Since the crest speed is 20 ml ph the translational momentum is — 

0-0278 X 202 = 11-1 w hr per ton. 
Thus, after allowing for the rotational momentum, we find that the 
total momentum is — 

11-1 X 1-09 = 12-1 w hr per ton. 



ENERGY CONSUMPTION 



53 



Still assuming that the train friction is negligible, and that the 
efficiency of the electrical equipment is 100 per cent., we have a 
consumption of — 

2 X 12-1 = 24*2 w hr per ton-mile, 

Now let us go to the other limit, i.e, to the lowest rate of 
accelerating and braking which will permit of obtaining the average 
speed of 20 ml ph for a 0'5-mile run. The speed-time diagram 
will be as in Fig. 29. 



40 



/o 































i 


A 




















/ 




\ 
















J 


/ 




\ 


\ 














/ 








\ 












/ 


/ 








\ 


\ 










/ 












\ 








/ 


f 












> 


\ 






/ 
















\ 








2 


6 


V< 


i) 


A 


J 


6( 


7 


K 


X> 



17me fn Seconcfs 

Fig. 29.— Speed-time Diagram for 0-5-mile Eun under Limiting Conditions. No 
Coasting Period and Minimum Acceleration and Declaration. 



The crest speed will be 40 ml ph, and will be attained in- 

-^=45 seconds. 

/. The acceleration is at the rate of — 

40 



45 



= 0-89 ml phps. 



The translational momentum at the crest speed will be — 

0-0278 X 402 = 44-5 w hr per ton. 
The total momentum = 44*5 x 1'09 = 48*5 w hr per ton. Neglecting 



54 



ELECTRIC TRAINS 



train-friction, and assuming 100 per cent, efficiency of the electrical 
equipment, the consumption at the train will be — 

2x48-5 = 97whr per ton-mile. 

Now let us take an intermediate case with the acceleration and 
deceleration both equal to 1*5 ml phps. The diagram is shown in 
Fig. 30. 



4/1 
























X 
























% 

■%20 




f 












\ 










1 












\ 








^10 


1 
















\ 






/ 
















\ 








/ 
















\ 







20 ^ 00 60 

77me in Seconds 



/OO 



Fig. 30. — Speed-time Diagram for 0'5-mile Run with no Track Friction. 
Acceleration and Braking of 1*6 ml phps. 



We have the formula — 

Crest speed = F = CT - -^/C^T^ - 7200 CM 

and from Table XV. we obtain — 

C = 0-75 

.-. F = 0-75 X 90 - x/o-563 x 8100 - 7200 x 075 x 0-5 
= 24*5 ml ph. 

Translational momentum = 0-0278 X 24*5^ = 16'7 w hr per ton 
Total momentum = 1*09 X 16-7 = 18'2 

= 36'4whr per ton-mile. 

Let us take one more case, employing the acceleration and 
deceleration of 1*0 ml phps. 

From this value we have, from Table XV. — 

C = 0-5 

F = 0-5 X 90 - ^0-25 X 8100 - 7200 X 0-5 X 0*5 == 30 ml ph. 



ENERGY CONSUMPTION 



55 



Translational momentum = 00278 X 30^ = 25*0 w hr per ton 
Total momentum = 1*09 X 25-0 = 27'2 „ 

= 54*4 w hr per ton-mile. 

Let us summarise these results as shown in Table XVIII. — 



Table XVIII. — Eneegy Consumption for a 0-5-Mile Run, with Vabious 
Values of Acceleration and Deceleration (assuming Frictionless Runs 
AND Electrical Equipment of 100 per cent. Efficiency). 



Acceleration 

and deceleration 

(ml phps). 


Crest speed 
(ml ph). 


Average speed 
(ml ph). 


Schedule speed 
(ml ph). 


Momentum energy at crest speed. 


whrperton. 


w hr per ton-mile. 


0-89 
1-00 
1-50 

Infinite 


40 
30 
24-5 
20 


20 
20 
20 
20 


16-3 
16-3 
16-3 
16-3 


44-6 
27-2 
18-2 
12-1 


97 
54-4 
36-4 
24-2 



Thus we see that, so far as the amount of energy required for 
momentum is concerned, we ought to employ as high an acceleration 
and deceleration as practicable. 

But, as we shall subsequently see, the employment of high 
accelerations imposes on the Electricity Supply Station, high peaks 
of load. As already stated, the commercially economical mean is, 
for city and suburban passenger trains, usually found to be some 
1*0 to 1"5 ml phps (see p. 5). 

Erom these considerations it is apparent that it is difficult to 
generalise as to the energy consumption at the train, corresponding 
to the maintenance of a given schedule speed, since the result 
depends very greatly indeed upon the acceleration and deceleration 
employed. 

It is obvious that an additional objection to the use of low 
values of acceleration and deceleration is the high crest value of 
the speed thus rendered necessary in obtaining a given schedule 
speed. 

A frequently recurring problem is, however, that relating to 
the lowest values of acceleration and deceleration which may be 
employed to obtain a given schedule speed for a given value of M, 
the distance from start to stop. Or, conversely, we may require to 
ascertain the highest schedule speed attainable, with accelerations 
and decelerations equal respectively, to stipulated values of A and B. 
To obtain this we may proceed as follows : — 

As in our preceding investigations, we may denote by E the 
crest value of the speed in ml ph. 



56 ELECTRIC TRAINS 

Then, for straight-line acceleration, we have — 

E 

Average speed (ml ph) = -^ 

E 

Time occupied by acceleration (seconds) = -r 

E 
„ „ braking (seconds) = ^ 

.*. Distance covered, in miles, is equal to — 

E /E E\ 
^ = 360(nr2iA + B) (See p. 47.) 

E^ A + B 
~" 3600 ^ 2AB 

/. E2 = 3600 X -f=^ X M 
A + B 

= 7200 X C X M 
and E = \/7200 x C X M 

E is the crest speed at the highest schedule speed corresponding to 
the stipulated conditions. 

A ^ /• 1 1.x \/7200 X C X M 
Average speed (m ml ph) = 



2 

Time occi 
run 



3ccupied by the entire 1 _ t _. 1! i Z = -p/ A + B \ 
from start to stop J "~ A B "" \ AB / 



But ^ = C 
• T = ? 



Also E = \/7200 X C X M. 
_ x/7200 X C X M 

T 

Now, the schedule speed = ^p , ^^ X average speed, where Q is the 

average duration of stop in seconds. 

Therefore, by substitution, we have — 

Limiting \ \/7200 X C X M \/7200 x C X M 

schedule speed \ - ^^^00 x C x M ^ ^\ "" 2 

(ml ph) J C X [^ g- + Qj 

3600 X C X M 



\/7200 X C X M + Q X C 



1 Enbbgy C 


PEED-TIME DiAGBAMS 






; Values of S, tl 




B = l-2 


B = 1'9 


B=2-0 




F 






F 


W 


S 


F 1 W 


•9 


36-6 




•6 


37-7 




15-7 


37-9 




•1 

•4 


60'4 
71-3 


7 


-2 
•2 


53-3 

75-5 


86-4 


23-3 
34-4 


53-6 
75-9 


87-2 


•0 


100-8 




7 


106-8 




50-0 


107-4 




r7 


37-9 




5 


40-5 




16-6 


40-8 




•3 

•4 


53-6 
75-9 


8 


•8 
•4 


57-3 
81-1 


99-5 


24-9 
36-6 


67-6 
81-6 


100 


•0 


107-4 




1 


114-6 




53-4 


115-3 




•3 


39-9 




3 


42-9 




17-4 


43-2 




•4 


56-4 


9 





60-7 


112 


26-2 


61-1 


103 


•9 


79-8 


3 


85-9 


38-6 


86-4 


1-4 


112-9 







121-5 




56-4 


122-2 




i-9 


41-5 







45-0 




18-1 


45-3 




•3 


58-8 


IC 


1 


63-7 


123 


27-2 


64-2 


124 


•2 

•4 


83-2 







90-4 




40-3 


90-7 




43-0 




•6 


46-9 




18-7 


47-3 




•0 


60-8 


11] 





66-3 


133 


28-2 


66-9 


135 


•4 


86-1 


'5 


93-8 




41-8 


94-6 




•8 


44-3 


•1 


48-5 




19-2 


49-0 




•7 


62-7 


'"it 


68-6 


143 


29-0 


69-3 


145 


•4 


88-6 


97-1 




43-0 


98-0 




•1 


45-4 


r6 


50-1 




19-7 


60-5 




p3 


64-2 


1^6 


70-8 


152 


29-8 


71-5 


155 


1-3 


90-9 







100-1 




44-4 


101-1 




^"5 


46-5 




1 


49-7 




20-2 


52-0 




•8 


65-7 


13 


3 


72-8 


160 


30-5 


73-5 


163 


•2 


92-9 





■4 


103-0 




45-4 


104-0 




•8 


47-4 


52-7 




20-6 


63-2 




•3 


67-0 


13 


•9 


74-6 


168 


31-1 


75-3 


172 


•9 


94-8 




9 


105-4 




46-3 


106-8 




•0 


48-2 




'8 


53-9 




20-9 


54-4 




•6 


68-2 


14 


■4 


76-2 


176 


31-7 


77-0 


179 


•5 


96-4 




\9 


107-9 




47-4 


108-9 




































^2 


49-0 


'0 


54-9 




21-2 


55-5 




^0 
'0 


69-3 


149 

7 


77-7 


183 


32-2 


78-6 


187 


98-0 


109-8 




48-2 


111-1 




'5 


49-7 


4 


56-0 




21-5 


56-6 




•3 


70-3 


144 
^4 


79-0 


189 


32-7 


80-0 


194 


•6 


99-3 


112-0 




48-9 


113-2 




^7 


50-3 


f6 


56-8 




21-8 


57-5 




\7 


71-2 


199 


80-4 


195 


33-2 


81-3 


200 


1 


100-7 


fl 

1 


113-6 




49-6 


115-0 




•9 


50-9 




}8 


57-7 




22-0 


58-4 




•0 


71-9 


1^ 


2 


81-6 


201 


33-6 


82-6 


206 


•6 


101-9 




9 


115-7 




50-4 


116-8 




1 49-7 




1 


58-4 




22-3 


59-2 




'•3 72-8 


1( 


6 


82-7 


207 


34-0 


83-8 


212 


•0 103-0 




3 


116-9 




50-9 


118-0 




•2 


52-0 




3 


59-2 




22-5 


60-0 




'5 


73-5 


1 





83-8 


212 


34-4 


84-8 


218 


5 


104-0 




•9 


118-0 




51-5 


120-0 























TabiiB XIX. Limiting Values ow Speed and Energy Consumption, neglecting Tbain-pbiction and assuming 100 per cent. Efpiciencx of Electrical Equipment, the Speed-time Diagrams 

HAVING NO Coasting Period (see Pigs. 29 and 32). 





M, 


Limiting Values of S, the Schedule Speed in ml ph ; F, the Crest Speed in ml ph ; and of W, the Train Consumption in w hr per Ton-mile, for Different Values of A, B, and M. 


the 
Acceleration 
(ml php8). 


Length 

Run 
(miles). 


B (the Deceleration 
during Braking) = 1 "0 


B=l-1 


B = l-2 


B = l-3 


B=r4 


B = l-5 


B=l-6 


B=1'7 


B=l-8 


8=1-9 


B=:2-0 


S 


F 


W 


s 


F 


W 


S 


F 


W 


S 


F 


W 


S 


F 


W 


S 


F 


W 


S 


F 


W 


S 1 F 


W 


S 


F 


W 


S 


F 


W 


S 


F 1 W 


0-5 


0-5 
1 
2 

4 


14-5 
21-5 
31'6 
46-0 


34-7 
49-0 
69-3 
98-0 


72-6 


14-7 
21-8 
32-0 
46-5 


35-2 
49-7 
70 '4 
99-5 


75-0 


14-9 
22-1 
32-4 
47-0 


35-6 
50-4 
71-8 
100-8 


77-0 


15-0 
22-3 
32-8 
47-5 


36-0 
51-0 
72-1 
102-0 


78-6 


15-1 
22-5 
33-1 
48-0 


36-4 

51-5 

72-9 

103-1 


80-1 


15-2 
22-7 
33-4 
48-5 


36-7 
52-0 
73-5 
104-0 


81-7 


15-3 
22-9 
336 
48-8 


37-0 
52-4 
74-1 
104-9 


83-0 


15-4 
23-0 
33-8 
49-1 


37-3 

62-7 

74-6 

106-6 


84-1 


15-5 
23-1 
34-0 
49-5 


37-5 
53-0 
76-1 
106-2 


86-2 


15-6 
23-2 
34-2 
49-7 


37-7 
53-3 
75-6 
106-8 


86-4 


16-7 
23-3 
34-4 
60-0 


37-9 
53-6 
75-9 
107-4 


87-2 


0-6 


0-5 
1 
2 
■1 


15-2 
22-7 
33-4 

48-5 


36-7 
62-0 
73-5 
104-0 


81-6 


15-6 
23-0 
33-9 
49-3 


37-4 
52-9 
74-7 
105-9 


84-5 


15-7 
23-3 
34-4 
50-0 


37-9 
53-6 
75-9 
107-4 


87-2 


16-9 
23-6 
34-8 
60-6 


38-4 
54-3 
76-9 
108-8 


89-6 


16-0 
23-8 
35-1 
51-1 


38-9 
55-0 
77-8 
110 


91-5 


16-1 
24-0 
35-4 
51-6 


39-3 
55-6 
78-5 
111-1 


93-5 


16-2 
24-2 
35-7 
62-0 


39-6 
56-1 
79-2 
112-1 


95-1 


16-3 
24-4 
36-0 
62-4 


39-9 
66-6 
79-9 
113-1 


96-5 


16-4 
24-6 
36-2 
52-8 


40-2 

56-9 

80-5 

113-9 


98-0 


16-6 
24-8 
36-4 
531 


40-6 
57-3 
81-1 
114-6 


99-5 


16-6 
24-9 
36-6 
63-4 


40-8 
57-6 
81-6 
115-3 


100 


0-7 


0-5 
1 
2 
4 


15'9 
23-6 
34-8 
50-5 


38-5 
54-4 
77-0 
108-9 


89-9 


16-0 
24-0 
35-4 
51-5 


39-0 
55-6 
78-4 
111-0 


93-2 


16-3 
24-4 
35-9 
52-4 


39-9 
56-4 
79-8 
112-9 


96-4 


16-5 
24-7 
36-4 
53-0 


40-5 
57-2 
80-9 
114-5 


99-1 


16-7 
25-0 
36-8 
53-6 


41-1 
58-0 
82-0 
116-0 


102 


16-9 
25-2 
37-2 
54-2 


41-5 
58-6 
82-9 
117-3 


104 


17-0 
25-4 
37-5 
54-7 


41-9 
69-2 
83-8 
118-5 


106 


17-1 
25-6 
37-8 
56-2 


42-3 

69-8 

84-5 

119-0 


108 


17-2 
25-8 
38-1 
55-6 


42-6 
60-2 
85-2 
120-6 


110 


17-3 
26-0 
38-3 
56-0 


42-9 
60-7 
85-9 
121-6 


112 


17-4 
26-2 
38-6 
56-4 


43-2 

Gl-l 

86-4 

122-2 


103 


0-8 


0'6 
1 
2 


16-4 
24-2 
36-1 


40-0 
50-6 
80-0 


96-7 


16-7 
24-8 
36-7 


40-8 
57-8 
81-7 


101 


16-9 
25-3 
37-2 


41-5 
58-8 
83-2 


105 


17-1 
25-6 
37-7 


42-2 
59-8 
84-4 


108 


17-3 
26-9 
38-2 


42-8 
60-6 
85-6 


111 


17-5 
26-2 
38-6 


43-3 
61-3 
86-7 


114 


17-7 
26-4 
39-0 


43-8 
62-0 
87-6 


116 


17-8 
26-7 
39-4 


44-2 
62-6 
88-6 


118 


17-9 
26-9 
39-7 


44-6 
63-2 
89-3 


121 


18-0 
27-1 
40-0 


45-0 
63-7 
90-4 


123 


18-1 
27-2 
40-3 


45-3 
64-2 
90-7 

47-3 
66-9 
94-6 


124 


0-9 


0'5 
1 
2 


16-8 
25-2 
37-1 


41-3 
58-4 
82-6 


103 


17-1 
25-6 
37-8 


42-2 
59-7 
84-4 


108 


17-4 
26-0 
38-4 


43-0 
60-8 
86-1 


112 


17-6 
26-4 
39-0 


43-7 
61-8 

87-6 


116 


17-8 
26-8 
39-5 


44-4 
62-8 
88-8 


119 


18-0 
27-1 
40-0 


45-0 
63-3 
90-0 


123 


18-2 
27-4 
40-5 


46-5 
64-4 
27-3 


126 


18-4 
27-6 
40-9 


46-0 
65-0 
91-9 


128 


18-6 
27-8 
41-2 


46-6 
65-7 
92-9 


131 


18 'C 
28-U 
41-5 


4G-9 
66-3 
93-8 


133 


18-7 
28-2 
41-8 


135 


10 


0-5 

1 
2 


17-2 
25-7 
38-0 


42-4 
60-0 
84-8 


109 


17-5 
26-2 
38-7 


43-4 
61-4 
86-8 


114 


17-8 
26-7 
39-4 


44-3 
62-7 
88-6 


119 


18-1 
27-1 
40-0 


45-1 
63-8 
90-2 


123 


18-3 
27-5 
40-6 


45-8 
64-8 
91-6 


127 


18-6 
27-8 
41-2 


46-5 
65-7 
92-9 


131 


18-7 
28-1 
41-6 


47-1 
66-6 
94-1 


134 


18-9 
28-4 
42-0 


47-6 
67-3 
95-2 


137 


19-0 
28-7 
42-4 


48-1 
68-0 
96-2 


140 


191 
28-9 
42-8 


48-5 
68-6 
97-1 


143 


19-2 
29-0 
43-0 


49-0 
69-3 
98-0 


145 


11 


0-5 
1 

2 


17-5 
26-2 

38-7 


43-4 
61-4 
86-8 


114 


17-8 
26-8 
39-6 


44-5 
63-0 
89-0 


120 


18-1 
27-8 
40-3 


46-4 
64-2 
90-9 


124 


18-4 
27-7 
41-0 


46-3 
65-4 
92-5 


130 


18-7 
28-1 
41-6 


47-1 
66-6 
94-2 


134 


18-9 
28-5 
42-2 


47-8 
67-6 
95-6 


138 


19-1 
28-8 
42-7 


48-4 
68-6 
96-9 


142 


19-3 
29-1 
43-2 


49-0 
69-4 
98-0 


145 


19-5 
29-4 
43-6 


49-6 
70-2 
99-2 


149 


19G 
29 G 
44-0 


50-1 
70-8 
lOO-l 


152 


19-7 
29-8 
44-4 


50-5 
71-6 
101-1 


155 


1-2 


0-5 
1 

2 


17-8 
26-7 
88-4 


44-3 
62-7 
88-6 


119 


18-1 
27-3 
40-3 


45-4 
64-2 
90-9 


125 


18-5 
27-8 
41-2 


46-6 
65-7 
92-9 


131 


18-8 
28-3 
41-9 


47-4 
67-0 
94-8 


136 


19-0 
28-6 
42-5 


48-2 
68-2 
96-4 


141 


19-2 
29-0 
43-0 


49-0 
69-3 
98-0 


145 


19-5 
29-3 
43-6 


49-7 
70-3 
99-3 


149 


19-7 
29-7 
44-1 


60-3 
71-2 
100-7 


153 


19-9 
30-0 
44-6 


50-9 
71-9 
101-9 


157 


201 
30-3 

45-0 


49-7 
72-8 
103-0 


160 


20-2 
30-5 
46-4 


62-0 
73-6 
104-0 


163 


13 


0-5 
1 
2 


18-1 
27-1 
40-0 


45-1 
63-8 
90-2 


123 


18-4 
27-7 
41-0 


46-3 
65-4 
92-5 


130 


18-8 
28-3 
41-9 


47-4 
67-0 
94-8 


136 


19-1 
28-7 

42-7 


48-3 
68-4 
96-7 


142 


19-3 
29-2 
43-4 


49-2 
69-7 
98-5 


147 


19-6 
29-6 
44-0 


50-1 
70-8 
100-2 


152 


19-8 
30-0 
44-6 


60-8 
71-7 
101-6 


156 


20-0 
30-3 
45-1 


51-5 

72-8 

103-1 


161 


20-2 
30-6 
45-5 


52 
73-7 
101-3 


165 


20-4 
30-9 
45-9 


52-7 
74-6 
105-4 


168 


20-6 
31-1 
46-3 


53-2 
75-3 
106-8 


172 


1-4 


0-5 

1 
2 


18-3 
27'5 
40-G 


45-8 
04-8 
91-6 


127 


18-7 
28-1 
41-6 


47-1 
66-6 

94-2 


134 


19-0 
28-6 
42-5 


48-2 
68-2 
96-4 


141 


19-3 
29-2 
43-4 


49-2 
69-7 
98-5 


147 


19-6 
29-6 
44-0 


50-2 
71-0 
100-4 


152 


19-9 
30-1 
44-7 


51-0 
72-2 
102-1 


158 


20-2 
30-4 
46-3 


61-8 
73-3 
103-6 


163 


20-4 
30-8 
46-9 


52-6 
74-36 
105-2 


167 


20-6 
31-1 
46-4 


63-2 
76-1 
106-5 


171 


20-8 
31-4 
46-9 


53-9 
76-2 
107-9 


176 


20-9 
31-7 
47-4 


54-4 
77-0 
108-9 


179 


1-5 


0-5 
1 
2 


18-5 
27-8 
41-2 


46-5 
(i5-7 
92-9 


131 


18-9 
28-5 
42-2 


47-8 
67-6 
95-6 


138 


19-2 
29-0 
43-0 


49-0 
69-3 
98-0 


145 


19-6 
29-6 
44-0 


50-1 
70-8 
100-2 


152 


19-9 
30-1 
44-7 


51-0 
72-2 
102-1 


158 


20-2 
30-5 
45-4 


52-0 
73-5 
104-0 


163 


20-4 
30-9 
46-0 


62-8 
74-7 
105-6 


169 


20-6 
31-3 
46-6 


53-6 
76-7 
107-1 


174 


20-8 
31-6 
47-2 


54-2 

76-7 

108-5 


178 


21-0 
31-9 
47-7 


54-9 
77-7 
109-8 


183 


21-2 
32-2 
48-2 


55-5 
78-6 
111-1 


187 


1-6 


0-5 
1 
2 


18-7 
28-1 
41-6 


47-1 
66-6 
94-1 


134 


19-1 
28-8 
42-7 


48-4 
68-5 
96-9 


142 


19-5 
29-3 
43-6 


49-7 
70-3 
99-3 


149 


19-8 
30-0 
44-6 


50-8 
71-7 
101-6 


156 


20-2 
30-4 
45-3 


51-8 
73-3 
103-6 


163 


20-4 
30-9 
46-0 


52-8 

74-7 
105-5 


168 


20-6 
31-4 
46-G 


63-6 
75-9 
107-4 


174 


20-9 
31-7 
47-3 


54-5 
77-0 
108-9 


179 


21-2 
32-1 
47-9 


56-2 

78-1 

110-6 


185 

190 


21-4 
32-4 
48-4 


66-0 
79-0 
112-0 


189 


21-5 
32-7 
48-9 


66-6 
80-0 
113-2 


194 


1-7 


0-5 
1 
2 


18-9 
28-4 
42-0 


47-6 
67-3 
95-2 


137 


19-3 
29-1 
43-2 


49-0 
69-4 
98-0 


145 


19-7 
29-7 
44-1 

19-9 
300 
44-6 


50-3 
71-2 
100-7 


153 


20-0 
30-3 
45-1 


51-5 
72-8 
103-1 


161 


20-4 
30-8 
45-9 


52-6 
74-3 
105-2 


1G7 


20-6 
31-3 
46-6 


53-6 
75-7 
107-1 


174 


20-9 
31-7 
47-3 


54-5 
77-0 
108-9 


179 


21-2 
32-2 
48-0 


66-4 
78-2 
1106 


186 


21-4 
32-5 
48-6 


56-1 
79-3 
112-0 


21 -G 
32-9 
49 1 


5G-8 
80-4 
113-6 


195 


21-8 
33-2 
49-6 


67-5 
81-3 
115-0 


200 


1-8 


0-5 
1 

2 


19-0 
28-7 
42-4 


48-1 
68-0 
96-2 


140 


19-5 
29-4 
43-6 


49-6 
70-2 
99-2 


149 


50-9 
71-9 
101-9 


157 


20-2 
30-6 
45-5 


52-0 
73-7 
104-3 


164 


20-6 
31-1 
46-4 


53-2 
75-1 
106-5 


172 


20-8 
31-6 
47-2 


54-2 
76-7 
108-5 


178 


21-2 
32-1 

47-9 


55-2 
78-1 
110-5 


185 


21-4 
32-5 
48-6 


56-1 
79-3 
112-0 


190 


21-6 
32-9 
49-3 


66-9 
80-5 
113-7 


196 


21-8 
33-2 
49-9 


57-7 
81-6 
115-7 


201 


22-0 
33-6 
50-4 


58-4 
82-6 
116-8 


206 


1-9 


0-5 

1 
2 


19-1 48-6 
28-9 G8-6 
42-8 97-1 


14 :J 


19-6 
29-6 
44-0 


50 1 
70-8 
100-1 


152 


20-1 
30-3 
45-0 


49-7 
72-8 
103-0 


160 


20-4 
30-9 
45-9 


52-7 
74-6 
105-4 


168 


20-8 
31-4 
46-9 


53-9 
76-2 
107-9 


176 


21-0 
31-9 
47-7 


54-9 
79-0 
112-0 


183 


21-4 
32-4 
48-4 


56-0 
79-0 
112-0 


189 


21-6 
32-9 
49-1 


56-8 
80-4 
113-6 


196 


21-8 
33-2 
49-9 


67-7 
81-6 
115-7 


201 


22-1 
33-6 
50-3 


58-4 
82-7 
116-9 


207 


22-3 
34-0 
50-9 


59-2 
83-8 
118-0 


212 


2-0 


0-5 

1 
2 


19-2 
29-0 
43-0 


49-0 

69-3 145 
98-0 


19-7 
29-8 
44-4 


50-5 
71-5 
101-1 


155 


20-2 
30-5 
45-5 


52-0 
73-5 
104-0 


163 


20-6 
31-1 
46-3 


53-2 
75-3 
104-0 


172 


20-9 
31-7 
47-4 


54-4 
77-0 
108-9 


180 


21-2 
32-2 
48-2 


55-5 
78-6 
111-1 


187 


21-5 
32-7 
48-9 


56-6 
80-0 
113-2 


194 


21-8 
33-2 
49-6 


57-5 
81-3 
115-0 


200 


22-0 
33-6 
50-4 


58-4 
82-6 
116-8 


206 


22 '3 
34-0 
50-9 


69-2 
83-8 
118-0 


212 


22-5 
34-4 
61-5 


60-0 
84-8 
120-0 


218 



To/ace p. 56.] 



ENERGY CONSUMPTION 



57 



The train consumption, making the 9 per cent, allowance for 
rotational momentum, is equal to — 

(0-0303 X r2) w hr per ton 
(218 X C X M) w hr per ton 



or 



= (218 



I w hr per ton-mile 



M 



= (218 X C) w hr per ton-mile. 

This result shows that the limiting train consumption per ton- 
mile for any given values of acceleration and deceleration is, under 
the assumed conditions, the same for any length of run. Q, the 
duration of stops, may usually be taken as 20 seconds. The highest 
attainable schedule speeds, and the corresponding crest values, have 
been calculated, by means of the above formulae, for runs of 0*5, 1, 2 




SO 



/CO y30 /so 200 

T/me /h <3econc/s 



290300 



Fig. 31.— Speed-time Diagram for 1-mile Run covered at Schedule Speeds of 12, 18, 
and 24 ml ph, with Constant Acceleration and Braking, and neglecting Train- 
friction. 

and 4 miles, and for various rates of acceleration and deceleration. 
The results are embodied in Table XIX. (folding table). 

As an instructive instance of the application of these principles, 
let us consider the case of a 1-mile run from start to stop, i.e. let 
us consider a case where M = I'O. Let us first study this run for 
schedule speeds of 12, 18, and 24 ml ph. The speed-time diagrams 
corresponding to these three schedule speeds, for A = I'O and B = 1*5, 
are readily worked out from the formulae and methods already 
described, and are plotted in Fig. 31. 



58 



ELECTRIC TRAINS 



Assuming 100 per cent, efficiency for the electrical equipment and 
negligible train-friction, the input required will be exclusively that 
corresponding in each case to the momentum at the crest speed, 
and may be obtained by the formula — 

Translational momentum = 0'0278 X F^ 

Total momentum = 0-0278 X I'OQ x F 

= 00303 X r2 w hr per ton 

where F is the crest speed in ml ph. The calculated values of the 
energy consumption for these three cases are shown in Table XX. — 



Table XX. — Eneegy Consumption for 1-mile Eun at Various Schedule Speeds, 

ASSUMING NO TRAIN-FRICTION AND 100 PER CENT. EFFICIENCY OF THE ELEC- 
TRICAL Equipment. 



Schedule speed 
(ml ph). 


F, the crest speed 
(ml ph). 


Train consumption 
(w hr per ton-mile). 


12 
18 
24 


13-5 
22-3 
36 


5-5 
15-0 

39-2 



It is evident that, with increasing speed, we are rapidly approach- 
ing a schedule speed which cannot be exceeded with the assumed 
values of acceleration, deceleration, distance between stops and dura- 
tion of stop. The limiting schedule speed is that at which the brakes 
must be applied at the very instant that the acceleration has been 
completed, i.e. there is in the corresponding speed-time diagram no 
interval of running at constant speed. For the assumed acceleration 
and deceleration, and for 20-second stops, this speed may be calcu- 
lated from the formula already given on p. 56, namely — 

3600 X C X M 

Limiting schedule speed = /r7o/>^ r^ ht : ~P^ 7^ 

* ^ V 7200 xCxM4-QxC 

For our case M = 1 and Q = 20. C may be obtained from Table XV. 
In this case, since A = I'O and B = 1*5 — 

C = 0-60 

2160 
.*. Limiting schedule speed = ~/^o7 ) i lo 

= 27-8 ml ph. 

Consequently, the time required for the 1-mile run from start to stop 
is — 



3600 
27-8 



20 = 109-6 seconds. 



ENERGY CONSUMPTION 



59 



The average speed is — 

109-6 + 20 
109-6 



X 27-8 = 32-8 ml ph. 



For this case, the speed-time diagram for which is drawn in 
Fig. 32, F, the crest value of the speed, is obviously equal to twice 
the average speed. Thus — 

F = 2 X 32-8 = 65-6 ml ph. 



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77me //? Seconds 

Fig. 32. — Speed-time Diagram for 1-mile Run under Limiting Conditions. No 
Coasting Period ; Acceleration and Deceleration of 1*0 and 1*5 ml phps 
respectively. 

We could have obtained F directly from the formula already given 
on p. 56, namely — 

E = ^7200 X C X M 
For M = 1-00 

C = 0-60 
.-. F = \/4320 = 65-6 ml ph. 

In order to obtain higher schedule speeds we must, obviously, 
resort to higher accelerating or decelerating rates, or both. Let us 
work out the case of a schedule speed of 30 ml ph, using an accele- 
rating rate of 1*3 ml phps and a decelerating rate of 1*8 ml phps. 
The calculation may be arranged in an orderly form as follows : — 



6o 



ELECTRIC TRAINS 



Schedule speed 

Length of run from start to stop 
Number of stops per hour . . 
Time at rest per hour .... 
Running time per hour . . . 
Time occupied by the 1-mile runi 

from start to stop .... J 30 

Accelerating rate 1*3 ml phps. 

Decelerating rate 1*8 ml phps. 

Let the crest speed be F ml ph. The values in Table XXI. are 
directly deduced. 



30 ml ph. 

1 mile. 

30. 

30 X 20 = 600 seconds. 

3600 -- 600 = 3000 seconds. 

= 100 seconds. 



Table XXI. — Showing the Duration op, and the Average Speed and 
Distance covered during, the Accelerating, Constant Speed, and 
Decelerating Periods of the Speed-time Diagram / in Fig. 33. 



Accelerating 
period 

Constant speed ■» 
period / 

Decelerating 
period 



Duration 

of run 

(seconds). 



1-3 

F F 

1-8 



Duration (hours). 



1 F^ 
8600^1-3 
1 / F F^\ 



1 ¥_ 
3600^1-8 



Average 

speed 
(ml ph). 



F 
2 

F 

F 
2 



Distance covered 
(mile). 



1 F^ F 
3600^1-3^ 2 
1 / F F\p 

300V 1-3~F8/ 



3600' 



1 ¥_ F 
3600^1-8^ 2 



600V: 



3600V2-6 



^^ = 1 



The total distance covered during the run is one mile- 

* lOOF - - — + 

1-3 1-8 ^ 3-67 

0-663r2 - 100F= -3600 
. pa _ 151 j^ ^ 5700 = -5430 + 5700 

F - 75-5 = +\/270 = +16-4 
F = 591 

Crest speed = 59*1 ml ph 

Time of accelerating period . . . . =45*5 seconds 

„ constant speed „ . . . . = 21*6 „ 

„ decelerating „ . . . . = 32*9 „ 

The results of all these five cases, together with results for the train 
consumption, in w hr per ton-mile (estimated from the formula, 
Momentum = 00278 X 109 x F^), are given in Table XXII., also 
values for a schedule speed of 27 ml ph. 



ENERGY CONSUMPTION 



6i 



Table XXII. — Energy Consumption of Trains stopping Once per Mile and 

RUNNING AT DIFFERENT SCHEDULE SPEEDS, ASSUMING NO TrAIN-FRICTION AND 

100 PER CENT. Efficiency. 



Schednle speed 
(ml ph). 


Acceleration 
(ml phps). 


Deceleration 
(ml phps). 


Crest speed 
(ml ph). 


Ratio of crest 

to schedule 

speed. 


Energy required 
(w hr per ton- 
mile). 


12 
18 
24 
27-8 


1-0 
1-0 
10 
1-0 


1-5 
1-5 
1-5 
1-6 


13-5 
22-3 
36-0 
65-6 


1-125 
1-24 
1-6 
2-37 


5-5 
15-1 
39-2 
131 


27 
30 


1-3 
1-3 


1-8 
1-8 


42-3 
59-1 


1-67 
1-97 


54 
106 



The corresponding speed-time diagrams are brought together in 



Fig. 33. 



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^ GO /20 /60 200 

77me /n Seconds 



2^fO 



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Fig. 38. — Speed-time Diagrams for 1-mile Run covered at the Various Schedules 

indicated. No Train-friction. 



In Table XXII. two different combinations of accelerating and 
decelerating rates are considered, but calculations have been made for 
other cases, and the results are given in Fig. 35, in which the values 



62 



ELECTRIC TRAINS 



of the amounts of energy required in w hr per ton-mile for these 
1-mile runs are plotted as ordinates, with the schedule speeds in ml ph 
as abscissae. The full lines represent the results for the separate values 



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^3chec^u/e S/beecf //t /n//o/f 

Fig. 34. — Curves of Train Consumption in w hr per ton-mile, assuming no Train- 
friction and 100 per cent. Efficiency of Equipment, for 0*5-mile Run and 
Various Schedule Speeds, with the Difierent Accelerations and Decelerations 
shown. 



of acceleration and deceleration, while the dotted line m is a mean 
curve drawn for a purpose, the utility of which will be obvious from 



the following considerations. 



ENERGY CONSUMPTION 



63 



For definite accelerations and decelerations we obtain correspond- 
ing curves for the energy required, with limiting values for each, 
corresponding to the cases where the constant-speed interval dis- 
appears. These limiting values are seen to lie on an even curve. 



aoox 




/6 



/a 



ZO 22 24^ 26 23 

Schedu/e S/oeecf mZ/i/t 



Fig. 35.— Curves of Train Consumption in w hr per ton-mile, assuming no Train- 
friction and 100 per cent. Efficiency of Equipment, for 1-mile Eun and 
Various Schedule Speeds, with the Different Accelerations and Decelerations 
shown. 



In Figs. 34 and 36 are plotted, for 0*5 and 2-mile runs, similar 
series of these curves for the same respective accelerations and 
decelerations indicated. The limiting values are again clearly shown 
at the top of the curves. 

Strict comparisons of the energy consumption for any given 
length of run, at the required schedule speed, should be made for 
various accelerations and decelerations, since Figs. 34, 35, and 36 



64 



ELECTRIC TRAINS 



indicate the important influence which these rates have on the 
consumption. 

For economic working, a train would not be run at the extreme 
limiting values shown in the curves. Nevertheless, the accelerations 
would be kept moderate, and the dotted curves m in Figs. 34, 35, 
and 36 are intended, in each case, to afford a locus for rational values 
for the range considered. 



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Fig. 36. — Curves of Train Consumption in w hr per ton-mile, assuming no Train- 
friction and 100 per cent. Efficiency of Equipment, for 2-mile Run and Various 
Schedule Speeds, with the Different Accelerations and Decelerations shown. 

These curves m, for 0'5-, 1-, and 2-mile runs, are brought together 
in Fig. 38, and show rational values for the energy consumptions in 
w hr per ton-mile. In Fig. 37 the corresponding values for the 
w hr per ton are plotted. 

Looking back to Fig. 34, relating to runs over distances of 0*5 mile 
from start to stop, we see that, neglecting train-friction and assuming 
100 per cent, efficiency for the electrical equipment, the energy con- 
sumption for a schedule speed of — for instance — 18 ml ph, may be 
anywhere from 50 w hr per ton-mile up to 100 w hr per ton-mile, 




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66 ELECTRIC TRAINS 

according as the mean of the acceleration and deceleration is nearer 
1*8 or 1*2 ml phps. 

Questions. — Chapter IV. 

1. Assuming a speed-time diagram as in Fig. 18, (a) What is the crest speed 
necessary to traverse a distance of 0*75 mile at an average speed of 20 ml ph, 
when the acceleration and deceleration are 0*8 and 1-7 ml phps respectively? 
(&) Find the energy input for momentum. 

Ans, (a) 23-9 ml ph. 

(&) 17 "3 w hr per ton. 

2. A distance of one mile has to be covered at 18 ml ph : A = 0*9, B = 1-8. 
(a) First running continuously, (h) then with one stop halfway, and (c) finally with 
two stops at one-third and two-thirds of the distance. 

The stops may be taken as at signals, but to be only of instantaneous duration. 
Determine the necessary crest speeds in these cases, using the formula of p. 48. 

Ans. (a) 20 ml ph. 
(h) 22 ml ph. 
(c) 27-4 ml ph. 

3. Repeat question 2, but take the stops as of 3 seconds' duration at each signal, 
and ascertain the crest speeds then necessary. 

Ans. (a) 20 ml ph. 
(&) 23-3 ml ph. 
(c) 33-5 ml ph. 

4. Following on the idea of question 2 : (a) Find the value of C which permits of 
five stops, one every one-fifth mile, for an instant, but under limiting conditions (as 
in Fig. 32). The crest speed will, of course, be 36 ml ph. (&) Given A = B, 
what will be the values of A and B ? 

Ans. (a) C = 0-9. 

(6) A = B = 1-8. 

5. Determine (a) the crest speed for the limiting run (similar to Fig. 32) over 
1000 m, when the values for acceleration and braking are respectively 0*8 and 1*5 
ml phps ; and (b) the schedule speed when the stop is of 20 seconds' duration. 

Ans. (a) 48*3 ml ph. 
(&) 20-0 ml ph. 

6. Under the assumed frictionless conditions, a train runs 1*20 mile at a schedule 
speed of 25 ml ph, and with a 20-second stop. Compare the energy consumptions, 
(a) when A = 1*0, B = 1-5; and (6) with the limiting speed- time diagram and 
A = B. 

Ans. (a) 36'6 w hr per ton for each run from start to stop. 
30*5 w hr per ton-mile. 
(&) 97*0 w hr per ton for each run from start to stop. 
80*8 w hr per ton-mile. 



CHAPTER y 

THE EFFICIENCY OF THE ELECTRICAL EQUIPMENT 

In Fig. 39 is given the experimentally observed speed-time diagram 
of a train weighing 72 tons, and equipped with four 150-hp motors. 
The train comprised one motor-coach and one trailer, and the speed- 
time diagram relates to a run of 1 mile from start to stop. In the 
tests, which were made by the engineers of the Lancashire and 
Yorkshire Eailway * on the electrified section between Liverpool and 
Southport, the 1-mile run was accomplished in 120 seconds. The 
average speed was thus — 

3600 -, on 1 . 
-j^TT X 1 = 30 ml ph. 

This, with 20-second stops, corresponds to a schedule speed of — 

190 
12^ X 30 = 25-7 ml ph. 

The input, measured at the train, was 77*7 w hr per ton-mile. 

From the speed-time diagram (Fig. 39) it is seen that the crest 
speed was 40 ml ph. Consequently, to supply momentum, there was 
required — 

0-0303 X 402 ^ 43.5 ^ hr per ton. 

The distance-time curve is shown in Fig. 40. Fifty-six seconds 
elapsed from the start up to the time when the electricity was cut off, 
and at the end of the 56th second the train had travelled 0*43 mile. 
Taking the train-friction as 6 kg per ton, then the portion of the 
input which is accounted for by train-friction was — 

0-43x1609x6 ..ox. 

^ . = 11*3 w hr per ton. 

The losses in the electrical equipment were consequently — 

77*7 - (48-5 4- 11-3) = 17*9 w hr per ton weight of train. 
The output from the electrical equipment amounted to — 
48-5 + 11-3 = 59-8 whr per ton, 

♦ " Proceedings of the Institution of Civil Engineers," vol. clxxix. pt. 1, p. 134. 

67 



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T/mC' in seconds 

Fig. 39. — Lancashire and Yorkshire Railway Speed-time Diagram for 1'0-mile 
Run at Schedule Speed of 25'7 ml ph. 



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Fig. 40. — ^Distance-time Curve corresponding to Fig.[.39. 



EFFICIENCY OF ELECTRICAL EQUIPMENT 69 

and, since the input was 77*7 w hr per ton, the efficiency of the 
electrical equipment, under the conditions of this particular run, 
was — 

^ X 100 = 76-9 per cent. 

This is rather a high efficiency and is not often attained. 

On p. 432 of Mr. Aspinall's Presidential Address, delivered before 
the Institution of Mechanical Engineers on April 23, 1909, another 
test made on the Lancashire and Yorkshire Eailway is quoted. This 
test was made on a 3 -coach train weighing 117 tons, and operated 
to a schedule speed of 30 ml ph, with 1 stop every 1*32 mile. The 
speed-time diagram was not given, but it is reasonable to conclude 
that it is fairly represented by Fig. 41. The corresponding distance- 
time curve is given in Fig. 42. The time occupied by a single run 
from start to stop is seen to have been 138 seconds. Consequently, 
the average speed was — 

- ^^^^^^ X 30 = 34-3 ml ph. 

The crest value of the speed is seen, from Fig. 41, to have been 49 
ml ph. The time elapsing from start to cut-off is 82 seconds, and 
the distance covered during this time is 0*75 mile, or 1200 m. 

The train, which, as already stated, weighed 117 tons, was com- 
posed of three coaches, two being motor- coaches and the third a 
trailer. Each motor-coach carried four 150-hp motors. Conse- 
quently, the complete electrical equipment comprised eight 150-hp 
motors and the auxiliary apparatus required for their operation. 
The input to the train worked out at 96 w hr per ton-mile. 

This input is made up of three components — 

I. Energy required for supplying momentum. This is equal to — 

0-0303 X 492 = 72-7 w hr per ton, 
and 

(1^9 ~)^^'^ ^ ^^ P®^ ton-mile. 

II. Energy required to overcome train-friction up to the point 
of cut-off. The electricity is cut off 82 seconds from the instant of 
starting, when the train has covered a distance of 1200 m(0*75 mile). 

The friction component is (assuming 6 kg per ton) consequently 

equal to — 

6 X 1200 ... , 

— -— — = 19*6 w hr per ton, 

and 

19-6 



I ytqo ~ |14*8 w hr per ton-mile. 



70 



ELECTRIC TRAINS 



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Fig. 41. — Lancashire and Yorkshire Railway Representative Speed-time Diagram 
for 1-32-mile Run at Schedule Speed of 30 ml ph. 



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Time in seconds . 



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Fig. 42. — Distance-time Curve corresponding to Fig. 41. 



EFFICIENCY OF ELECTRICAL EQUIPMENT 71 



III. Energy transformed from electricity into heat in the electrical 
equipment. This equals 96*0 — (55*0 + 14'8) = 26'2 w hr per ton-mile. 

The output from the electrical equipment is the sum of the 
momentum at the crest speed and of the train-friction up to the 
instant of cut-off, and is equal to — 

55-0 + 14-8 = 69-8 w hr per ton-mile. 
Since the input is 96*0 w hr per ton-mile, the efficiency is equal to — 

^ X 100 = 72-6 per cent. 

Let us further examine these two sets of results, i.e. the results 
of the tests on the 72-ton and 11 7- ton Lancashire and Yorkshire 
trains. The leading data is brought together in Table XXIII. — 

TabiiE XXIII. — Analysis of Train Tests on the Lancashire and Yorkshire 

Railway. 



Weight of train (ton) 

Distance between stops (mile) 

Schedule speed, assuming 20-second stops (ml ph) 

Crest speed (ml ph) 

Energy required for momentum (w hr per ton-mile) . 

Number of seconds elapsing up to cut-off .... 

Distance up to point of cut- off (mile) 

Energy required for train-friction up to point of cut-ofi 
(w hr per ton-mile) 

Energy required to supply the losses in the electrical equip- 
ment (w hr per ton-mile) 

Input to train (w hr per ton-mile) 

Efficiency (per cent.) 



72 


117 


1-00 


1-32 


26-7 


80-0 


40 


49 


48-5 


55-0 


56 


82 


0-43 


0-75 


11-3 


14-8 


17-9 


26-2 


77-7 


96-0 


76-9 


72-6 



The next steps of interest relate to the average input to the 
motors in the two cases. These are set forth in Table XXIV. — 

Table XXIV. — Continued Analysis op Train Tests on the Lancashire and 

Yorkshire Railway. 



Weight of train (ton) 

Input per train-mile (kw hr) 

Ditto in kw hr per hour, i.e. average kw input 

Efficiency (from Table XXIII.) 

Average output (kw) 

Number of motors per train 

Average output per motor, taken over entire run (hp), m 

Ditto in per cent, of rated load 

Number of seconds elapsing from start to " cut-ofi " of 

electricity 

Number of seconds elapsing from start from one station to 

start from next station 

Ratio of time during which train is consuming electricity 

to entire time of run, n 

Average output per motor, during the time it is in circuit 

(hp) m -T-n 

Ditto in per cent, of rated load 



72 


117 


5-60 


11-2 


144 


336 


0-769 


0-726 


111 


244 


4 


8 


37-2 


40-9 


24-8 


27-2 


66 


82 


140 


158 


0-400 


0-519 


93 


79 


62-0 


52-6 



72 



ELECTRIC TRAINS 



The lower point of the efficiency curve at which the motors are 
working, as the result of the lower percentage of the rated load 
which they are carrying while in circuit, suffices to account for about 
half of the 4 per cent, lower over-all efficiency of the electrical 
equipment observed in the case of the 117-ton train. That this is 
the case will become clear by an examination of the efficiency curves 
of typical 150-hp series-wound railway motors. The curves, which 
correspond respectively to the operation of the motor at 250 volts 
(corresponding to the full series position of the controller) and at 
600 volts (corresponding to the full parallel position of the con- 



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240 



Fig. 43. — Eepresentative Efficiency Curves for a 150-hp Continuous Electricity Rail- 
way Motor on 500 volts (Parallel) and 250 volts (Series). 
Curve jB, Excluding Gear. 
,, G, Including Gear. 

troller), are shown in Fig. 43. The results for 62 per cent, and 52-6 
per cent, of rated load (from Table XXIV.) are as follows : — 



Efficiency at 250 volts 
„ 500 „ 



Load on motor. 



62 per cent, of rated 
load (93 hp> 



63*0 per cent. 
89-0 



52 '6 per cent, of rated 
load (79 hp). 



700 per cent. 
87-5 



EFFICIENCY OF ELECTRICAL EQUIPMENT 73 

The motors were in the series position for only some 10 to 15 
seconds from the moment of starting, and during this time they were 
in series with resistances up to the very last few seconds. On the 
other hand, the motors were in parallel for some 45 to 65 seconds, and 
for most of this time they were running without resistances in series, 
i.e. they were running with about 500 volts at their terminals. Conse- 
quently, the average efficiencies of the motors for the entire run were 
far more influenced by the efficiencies in the parallel position, i.e, the 
500-volt efficiencies, than by the 250-volt efficiencies. Taking into 
account the widely varying loads to which motors are subjected from 
instant to instant in a service of this kind, it appears sound to assess 
at 2 per cent, the amount by which the average motor efficiency for 
the entire run is less at 52*6 per cent, of rated load than at 62 per 
cent, of rated load. 

Of the 4 per cent, lower over-all efficiency of the equipment, 
there is, in addition to the 2 per cent, just estimated, a further 2 per 
cent., which is accounted for as follows. 

It will be observed that, during the first 20 seconds from the 
start, the 72-ton train was brought to a speed of 26 ml ph as against 
a speed of only 21 ml ph for the 117-ton train. The average acceler- 
ations for the two cases for the first 20 seconds were, consequently, 
1'30 and 1'05 ml phps respectively. Now, the more rapid the acceler- 
ation the more quickly will the regulating rheostats, employed in 
series with the motors during starting, be cut out, and in the case of 
the test of the 72-ton train, the rheostats are known to have been 
finally cut out in the parallel operation only 15 seconds from the 
instant of starting the train, whereas, for the 117-ton train, the rheostats 
were probably in circuit (although this is only to be regarded as in 
the light of a reasonable estimate) for at least 30 seconds from starting 
the train. Consequently, losses were occurring in the controlHng 
rheostats for only 10 '7 per cent, of the entire time in the case of the 
72-ton train, as against some 19 per cent, of the entire time in the 
case of the 117-ton train. In the latter case the rheostatic loss 
would have been sufficiently greater than in the former case to amply 
account for the remaining 2 per cent, deficit in the efficiency. 

The points involved in the preceding paragraphs are of great 
importance. In the test of the 117-ton train, in spite of the severity 
of the schedule, the acceleration and the deceleration during braking 
have been kept within the limits of the best practice to which conform- 
ance can be made in routine daily service. In the test of the 72-ton 
train, however, the acceleration and the deceleration are well up to, and 
in fact are decidedly beyond, the all-round desirable values. Thus, the 
rate of deceleration during the last ten seconds of the run of the 
72-ton train is seen from Fig. 39 to be of the very high value of 
2*7 ml phps, while in the case of the 117-ton train, the deceleration 



74 ELECTRIC TRAINS 

during the last ten seconds (Fig. 41) is at an approved rate, being 
1*8 ml phps. 

In the test with the 72-ton train the object has been to keep the 
crest speed down to a low value, with a view to obtaining a high 
efficiency. This has been accomplished by resorting to very high 
acceleration and deceleration. On the whole, the 76 '9 per cent, 
efficiency obtained for the test run with the 72 -ton train must be 
regarded as abnormal, since resort was made to exceedingly high 
acceleration and deceleration. The average outputs, taken over the 
entire run, and allowing for 20-second stops, are 37*2 hp for the 72- 
ton train and 40*9 hp for the 117-ton train. In terms of the rated 
load, these values work out at 24"8 per cent, and 27*2 per cent, 
respectively. 

The question of motor heating is taken up again in Chapter XIL, 
but let us at this point accept provisionally, for our present purposes, 
the rough rule that for a given service where the only intervals of 
rest are the 20-second stops at stations, and where each motor- 
coach must operate to its schedule for 18 consecutive hours, an 
aggregate rated capacity of electrical equipment equal to four times 
the average load must be provided. On the basis of the conventional 
method of rating railway motors, this will give reasonable assurance 
that the maximum temperature-rise above the temperature of the 
surrounding air will, in the conditions of actual service on the train, 
not appreciably exceed 65° C. 

In the conventional basis of rating of railway motors it is required 
that after a one-hour test on a stand at the manufacturer's works at 
rated load (and with the covers over the commutator open), the 
temperature-rise of the hottest accessible part, as thermometrically 
determined, shall not exceed by more than 75° C, the temperature of the 
surrounding atmosphere. This is a purely nominal basis of rating ; 
nevertheless, it has been proved, in the course of the many years 
during which it has been employed by all the leading manufacturers 
of railway motors, that it constitutes an excellent basis on which to 
rate motors. This 1-hour, 75° 0. load, while it is of the order of four 
times the average load for which the motor is thermally suitable for 
a service of several consecutive hours, is a load well within the 
motor's capacity as regards mechanical construction and commutation. 
For brief periods during starting, a motor usually has to carry a load 
well up toward, or even above, its 1-hour, 75° C. rating ; consequently, 
it is important that at its rated load the performance of the motor 
shall be excellent as regards commutation. 

Corresponding to the efficiency investigations set out above for 
the Lancashire and Yorkshire equipments under the conditions of 
service, I have carried out a number of investigations of the working 



EFFICIENCY OF ELECTRICAL EQUIPMENT 75 

efficiencies of the train equipments on several other electric railways.* 
The results indicate that for services where the trains operate at 
high schedule speeds with frequent stops, the over-all efficiency of the 
electrical equipment on the train should, in actual practice and for 
correctly driven, correctly proportioned trains and equipments, be of 
the order of 70 per cent. While it is often quite exact enough to 
employ this figure in estimates, nevertheless, I have attempted to 
assess more precise values for particular services, since the over-all 
efficiency is, in practice, a function of the length of run between stops, 
the schedule speed, and the acceleration and deceleration. The 
values at which I have arrived are set forth in Table XXV., and may 

Table XXV. — Ovee-all Efficiencies op Electeical Equipment foe Vaeious 

Schedule Speeds and Runs. 





Mean of Acceleration and Deceleration. 


Schedule speed 




1 '0 ml phps. 




1 '5 ml phps. 




1 "8 ml phps. 




















stop (ml ph). 


Distance between stops 


Distance between stops 


Distance between stops 






(miles). 




(miles). 




(miles). 






0-5 


1-0 


2-0 


4-0 


0-5 


10 


2-0 


4-0 


0-5 


1-0 


2-0 


40 


10 


76 








74 


76 






74 


76 






15 


71 


75 


78 


— 


72 


75 


77 


— 


72 


75 


77 


— 


20 


68 


72 


76 


78 


70 


73 


76 


79 


70 


73 


76 


79 


25 


65 


70 


74 


77 


67 


71 


75 


78 


67 


71 


75 


78 


30 


— 


68 


72 


76 


65 


69 


73 


77 


— 


70 


74 


77 


35 


— 


65 


71 


74 


— 


67 


72 


75 


— 


68 


73 


76 


40 


— 


— 


69 


73 


— 


66 


71 


74 


— 


67 


72 


75 


45 


— 


— 


67 


71 


— 


— 


70 


73 


— 


— 


71 


74 


50 


— 


— 


— 


70 


— 


— 


68 


72 


— 


— 


69 


73 


55 


— 


— 


— 


68 


— 


— 


67 


71 


— 


— 


68 


72 



be taken to apply to series -parallel equipments employing geared, 
series-wound, continuous-electricity motors, designed for operation 
without forced draught and proportioned for a load which, averaged 
over their period of daily service, amounts to 25 per cent, of their 1- 
hour, TS'" C. rated load. Equipments worked up to a higher average 



* Among other electric railways which I have investigated in this manner may be 
mentioned the following : — 

Hey sham, Morecambe and Lancaster section of the Midland Railway. " Proceedings 
Institution of Civil Engineers," vol. clxxix. pt. 1, p. 31. 

South- Side Elevated Railway of Chicago. " Transactions of the American Institute 
of Electrical Engineers," vol. xvi. p. 193. 

General Electric Company (U.S.A.) Experimental Track. Ibid. vol. xix. p. 831. 

New York and Port Chester Railway Company (U.S.A.). Ibid. vol. xix. p. 180. 

Grand Rapids, Grand Haven and Muskegon Railway. Ibid. vol. xxiii. p. 691. 

Vienna-Baden Railway. Electrical Engineering, December 12, 1907. 



76 



ELECTRIC TRAINS 



load than this, i.e. equipments not proportioned to be thermally 
capable of sustaining for several hours the schedule as regards speed, 
number of stops, and duration of stops, will, if correctly designed and 
operated, have higher efficiencies than those indicated in Table XXV., 
whereas equipments where the average load is less than 25 per cent, 
of the rated load will have lower efficiencies than those indicated in 
Table XXV. Equipments employing gearless motors will have 
higher efficiencies than those indicated in Table XXV. Single-phase 
equipments of the best types yet commercially developed will, for 
services with high schedule speeds and frequent stops, have only 
slightly lower efficiencies than those indicated in Table XXV. 









Length of Run 'between stops 






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Fig. 44. — Kepresentative Speed-time Diagrams for Various Schedule Speeds and 
Euns under Working Conditions. 

The influence on the over-all efficiency of the average load carried 
by the equipment during the time it is in circuit is very considerable, 
as may be seen from the curve in Eig. 60, on p. 105 of Chapter VII. 
Indeed, in support of the exaggerated claims made for the single- 
phase motor as applied to severe services {i.e. for services for high 
schedule speeds and frequent stops), tests have been made with 
electrical equipments which, during the runs, were carrying so great 
a load that the schedule speed could not have been maintained for 



EFFICIENCY OF ELECTRICAL EQUIPMENT 77 

much over two hours without exceeding desirable limits of tempera- 
ture rise. In view of the fundamental considerations indicated in 
this chapter, the reader will appreciate that equipments overloaded 
in this manner will have higher efficiency than when operated at 
the conservative loads corresponding to sound practice as regards 
temperature rise. ^Nevertheless, even under these conditions, the 
single-phase equipments which I have in mind, namely those in 
operation on the Heysham Branch of the Midland Eailway, only 
developed over-all efficiencies of the order of 68 per cent, to 72 per 
cent. There is but little to choose between continuous and single-phase 
equipments as regards their efficiency under the conditions of actual 
service, but any superiority in this respect which there may be is 
certainly possessed by continuous equipments. This cannot be too 
emphatically pointed out, since utterly unfounded statements have 
been made to the contrary by various engineers. The reader may be 
interested in this connection to look up an article on p. 341 of the 
Light Railway and TraWjWay Journal for June 11, 1909 ; also a 
letter in the Railway Gazette for July 2, 1909, where he will find 
typical instances of the unfounded claims to which I allude. 

Fig. 44 consists of a chart of speed-time diagrams which are 
representative of preferable practice for the corresponding schedule 
speed and number of stops. By employing the data and methods 
set forth in the preceding chapters, together with the efficiency values 
given in Table XXV., the estimations set out in Table XXVI. have been 
made. These estimations relate in the first instance to the energy 
consumptions at the train, corresponding to the speed-time diagrams of 
Fig. 44, and at the end of the table estimates of the rated capacity of 
electrical equipment which should be installed for each schedule are 
worked out.* 

The results obtained in Table XXVI. are plotted in the curves of 
Figs. 45 to 48. 

* The subject of energy consumption of trains running to different schedules, as 
also of the motor capacity to be installed, is dealt with by 0. T. Hutchinson, in a 
paper entitled " The Relation of Energy and Motor Capacity to Schedule Speed in 
the Moving of Trains by Electricity," which was read before the American Institute 
of Electrical Engineers, vide " Transactions," vol. xix. p. 129. See also a paper by 
W. B. Potter on " The Selection of Electric Motors for Railway Service " {ibid. 
p. 169). 



78 



ELECTRIC TRAINS 



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EFFICIENCY OF ELECTRICAL EQUIPMENT 79 



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Schedule Speed /n/n/fih 



PiQ. 45. — Curves giving Conservative Estimates of the Energy Consumption at the 
Train for Various Schedules, under Normal Working Conditions (from Calcu- 
lations of Table XXVI., based on the Curves in Fig. 44). 



EFFICIENCY OF ELECTRICAL EQUIPMENT 8i 




/5 :do e^ 30 

3chedu/e Speed /n m/ jo/t 



Fig. 46. — Curves giving Conservative Estimates of the Capacity of Equipment in 
Rated hp of Motors per Ton Weight of Train, necessary for operatiag Various 
Schedules under Normal Working Conditions. 



82 



ELECTRIC TRAINS 




Stoji>s per ^/Je 0,S 



W"^ 



1 



Fig. 47. — Curves giving Conservative Estimates of the Energy Consumption at the 
Train for Various Schedules, under Normal Working Conditions (from calcu- 
lations of Table XXVI. based on the Curves in Fig. 44). 



EFFICIENCY OF ELECTRICAL EQUIPMENT 83 




Stoj»/9erflfj/e 0,S /,0 



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Fig 48.— Curves giving Conservative Estimates of the Capacity of Equipment in 
Rated hp of Motors per Ton Weight of Train, necessary for operating Various 
Schedules under Normal Working Conditions. 



84 



ELECTRIC TRAINS 



Table XXVII. gives a specification for a typical four-coach 
Lancashire and Yorkshire train, and Fig. 49 is a photograph of the 
train. This four-coach train is employed both for a stopping service 
with runs of an average length of 1*32 mile between stations, in which 
case the schedule speed is 30 ml ph, and for an express service with 
a schedule speed of 44*5 ml ph, making one intermediate stop in the 
total run of 18*5 mile.* 



Table XXVII.— Specification op Foue-Coach Train on Lancashire and 

Yorkshire Railway. 

A. — Motor-Coach. B. — Trailer-Coach. C. — Complete Four-Coach Train. 

A. — Motor-Coach. 
General — 

Total length over buffers 62 ft 9| in 

„ „ framework . . . . . . . 60 f 1 4f in 

Length between centres of trucks . . . . . . 40 ft 6 in 

,, of motor compartment . . . . . . 4 f 1 6| in 

,, of luggage compartment . . . . . . 6 ft 5| in 

,, of passenger compartment . . . . . . 42 ft 5 in 

There are two divisions in the passenger compartment, with a door between. The 
main doors are situated at the ends of the compartment. 

Height, over-aU, above rail level . . . . . . 12 ft 7J in 

„ of driver's cab floor above rail level . . . . 4 ft 4? in 

,, of passenger floor „ „ . . . . 4 f t 4| in 

„ of centre of gravity of coach above rail level . . 3 ft 9 in 

Width, over-all, outside . . . . . . . . 10 ft in 

Seating capacity (3rd Class) ........ 69 

Weight of coach without passengers ..... 46 tons 

„ of car body, including under-frame, air compressors, seats, 

upholstering, and aU fittings ..... 22'5 tons 

Seats per foot length of coach . . . . . . . 1-14 

„ per ton weight of coach . . . . . . . 1*5 

Trucks — 

Both trucks on the motor-coach have each of their axles driven by motors, and are 
similar. 



Weight of motor-truck without motor 
,, of complete motor-truck 
„ sustained per axle on rail 

Wheel-base of truck 

Gauge of truck 

Diameter of driving wheels 



6*11 tons 

12-45 tons 

11'5 tons 

8 ft 

4 ft 81 in 

3 ft 6 in 



Messrs. Dick-Kerr 
150 



Electrical Eqtdpment — 

Type or make of motor ...... 

Bated hp ....... . 

Method of control is the Dick-Kerr direct system. The two motor-coaches carry 
the electrical equipment at the ends of the train. A number of coaches are also 
arranged for Multiple Unit System of control. 



♦ For a description of the electrification of the Lancashire and Yorkshire Railway 
the reader is referred to Mr. J. A. F. Aspinall's Presidential Address to the Institution 
of Mechanical Engineers ('* Proceedings, Institution of Mechanical Engineers," 1909, 
No. 2, pp. 423-491). 



EFFICIENCY OF ELECTRICAL EQUIPMENT 85 



Particulars of Gear on Motors — 

Spur wheel 43 teeth 

Pinion 22 teeth 

Gear ratio .......... 1"95 

Weight of gear with case, about 122 kg 

Weight of one motor alone ....... 2'75 tons 

,, of motor and gear ....... 2*86 tons 

Number of motors per motor-coach . . . . . . .4 

Total weight of motors with gearing per motor-coach . . 11*7 tons 
Weight of balance of electrical equipment {i.e. con- 
trollers, rheostats, etc.) per motor-coach .... 2*99 tons 

Total weight of electrical equipment per motor-coach . . 14*69 tons 
Ratio of total weight of electrical equipment to weight 
of motors and gearing . . . . . . . . . 1*24 

Weight of motor in kg per hp (rated) ...... 18*6 

„ of motor and gear in kg per hp (rated) .... 19-4 

,, of motors and gear in kg per ton weight of motor-coach . 259 

, , of aU electrical equipment in kg per ton weight of motor-coach 323 

Ratio of total weight of electrical equipment to weight of motor-coach 0*323 



B. — Tbailer-Coach. 



Length over framework . 

,, between centres of trucks . 
Total length of passenger compartment 
Divisions of passenger compartment 



60 ft in 

40 ft 6 in 

53 ft in 

.2 



Arrangement of doors is similar to motor-coach — at the ends of the compart- 
ments. 



Height of top of coach above rail level 

,, of floor above rail level 
Width, over-all, outside . 
Number of seats per coach (alternative) 



Weight of traUer-coach {a and b) 

>> >> >> (C/ 

Seats (1st Class) per foot of length of coach 

„ „ per ton of weight of coach 



. 12 ft 71 in 

. 4 ft 4J in 

10 ft in 

1st Class, 66 (a) 

3rd „ 80 (&) 

3rd „ 90 (c) 

26 tons 

. 27-58 tons 

. 1*10 

. 2*54 



C. — Complete Train. 



Number of motor-coaches 

„ of trailer ,, 
Total length of train over buffers 

„ weight of train without passengers 
Weight of motor-coach component . 

,, of trailer-coach ,, 

Total seating capacity 



.2 

. ■ .2 

248 ft 6 in 

144 tons 

92 tons 

52 tons 

270 



The motor-coaches are fitted with third-class seats, while there are trailer - 
coaches of both first- and third-class seats. 



The seating capacities are — 

(1) 2 motor-coaches, 3rd class 4- 2 trailer-coaches, 1st class = 270 seats. 

(2) „ ,, „ -i- 1 trailer, 1st class + 1 trailer, 3rd class = 

seats. 

(3) „ ,, ,, 4-2 trailer-coaches, 3rd class = 298 seats. 



284 



86 



ELECTRIC TRAINS 



The first alternative is more general. 

Number of motors per train .... 
Total hp per train ..... 

„ weight of motors and gearing 

Weight of electrical equipment (motor-coach) 
,, ,, ,, (trailer-coach) 



Total weight of electrical equipment per train 

Seats per foot length of train (270 seats) . 
,, per ton weight of train 

Rated hp per ton of train .... 
,, per seat of train .... 

Total weight of motors and gearing in kg per ton of train 
„ „ „ ,, in kg per seat of train 

„ >» of electrical equipment in kg per ton of train 

,, ,, ,, „ in kg per seat of train 

Ratio of total weight of electrical equipment to total train weight 



.8 

. 1200 

23-39 tons 

29-375 tons 

0-575 ton 



29 



95 tons 
1-08 
1-87 
8-33 
4-44 
165 
88-7 
210 
113 
0-21 



The braking equipment consists of combined automatic, vacuum, and hand 

systems. 




Fig. 49. — Standard 4-Coacli Lancashire and Yorkshire Train. 



\Tofac(i j). 86. 



I 



CHAPTER VI 

THE DETERMINATION OF THE EFFICIENCY OF THE ELEC- 
TRICAL EQUIPMENT OF THE TRAINS ON THE CENTRAL 
LONDON RAILWAY 

The Central London Eailway* is built with grades sloping down 
from the out-going end of the platform, and rising up to the arriving 
end of the platform. Throughout the length of the platform the 
track is level. The line originally extended from Shepherd's Bush 
to the Bank, and is 5*77 miles in length between those two stations. 
There are 11 intermediate stations, which, together with the two 
terminal stations — namely. Shepherd's Bush and Bank — make a total 
of 13 stations. The average distance between stations is — 

^ = 0-48 mile. 

The sketch in Fig. 50 is typical of the gradients on a repre-" 
sentative section of 0'48 mile (772 m) length. On leaving the 



TTTTTP.^'ZTPZ' 



Direction of Running 










M5. 



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yert/caJ Sc^Je - 20 T^mea /fonzonbjt/ Sca/a 

Fig. 50. — Typical Gradients on a Section of 0-48 mile (772 m) on the Central 

London Railway. 

station, every ton of weight of train experiences, during the time 
that electricity is being absorbed from the supply, a vertical fall 

* A very complete description of the Central London Railway, accompanied by 
173 illustrations, was published in Traction and Transmission, Nos. 29-31, 1903, by 
H. F. Parshall, E. Parry, and W. Casson. 

87 



88 ELECTRIC TRAINS 

of 2 '4 m. Thus, in addition to the energy transformed from 
electricity into momentum and into heat, there is a certain amount 
of energy transformed from potential energy of altitude into mo- 
mentum and into heat. This latter amount is equal to 2*4 ton- 

meters, or 2400 kg m or ( ^ „ = p'Q w hr per ton weight of train. 

Since the distance between stops is 0*48 mile, this potential energy 
of altitude works out at — 

■pr-r^ = 140 w hr per ton-mile. 
0'48 ^ 

By means of wattmeters on the train, measurements have been 
made of the total amount of electricity consumed during complete 
round trips from Shepherd's Bush to the Bank and back to Shepherd's 
Bush. The train, in the course of a complete round trip, started 
from a siding just beyond Shepherd's Bush station and pulled into 
Shepherd's Bush, where it stopped for passengers. After discharging 
its passengers at the Bank, the train ran into a siding just beyond 
the Bank station, stopped there, and returned to the Bank station, 
where it stopped to take on passengers. After discharging its 
passengers at Shepherd's Bush it again pulled into the siding and 
stopped. A complete round trip thus involved starting the train 
28 times. But in 4 out of these 28 starts it was only required to 
run the train up to a slow speed, and to traverse a very short 
distance. We may take these four operations as equivalent to one 
normal run over a 0*48-mile section so far as relates to energy 
consumption. Thus, we may analyse these round trips as if they 
had comprised 25 runs, each of 0*48 mile in length. For the pur- 
poses of tests, runs were made occupying 22 minutes for the journey 
from Shepherd's Bush station to the Bank station, and also occupying 
22 minutes for the return journey from the Bank station to Shepherd's 
Bush station. Since the distance each way is 5*77 miles the schedule 
speed is — 

1^ X 5-77 = 15-7 ml ph.* 

The stops between stations were of 15 seconds' duration. A train 
making a schedule speed of 15 '7 ml ph, and with a stop every 048 
mile, makes stops at the rate of — 

^ = 32-8 per hr. 

Thus, if the train ran continuously to this schedule, the aggregate 
duration of the 32*8 stops per hour would amount to (32*8 x 15 = ) 



CENTRAL LONDON RAILWAY 



89 



492 seconds. Consequently, the train would be in motion during 
(3600 - 492 =)3108 seconds out of the 3600 seconds in each hour. 
The time elapsing from start to stop is thus — 

oo.Q =95 seconds. 

Thus, we have — 

T = 95. 

The average speed, i.e. the average speed between stations, is thus — 

95 +15 



95 



X 15-7 = 18-2 ml ph. 



No exact measurements were made of the crest value of the speed, 
but the speed-time diagram shown in Fig. 51, drawn to comply with 























— ■ 
























































































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— 


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20 



-«7 eo 

TJmc in Sefone/s 



Fig. 51. — Typical Speed-time Diagram for 0-48-mile Run.at Schedule Speed 

of 15-7 ml ph. 



the above-stated average speed, and for M = 0*48 and T = 95, must 
evidently be a close approximation to the truth. The crest speed of 
this speed-time diagram is 25*5 ml ph. Electricity is supplied to 
the train during the 48 seconds required to attain this crest speed. 
At that point the electricity is cut off, and during the remainder 
of the journey the propulsion-energy is supplied from the momentum 
of the train. At the crest speed (25*5 ml ph), the momentum of 
the train is — 

0'0278 X 1-09 X 25-52 = 19-7 w hr per ton. 



90 



ELECTRIC TRAINS 



The energy required to supply momentum is thus — 

19'7 

Y^^ = 41*0 w hr per ton-mile. 

For the first 48 seconds, during which the energy required for over- 
coming train-friction is obtained from the supply of electricity and 
from the potential energy of altitude, the average speed is ascertained 
from Fig. 51, to be 17*1 ml ph. The distance covered during this 
time is consequently some — 

48 
^^ X 17-1 = 0-228 mile = 366 m. 

Taking the train- friction at 6 kg per ton, our estimate of the energy 
required for train-friction is — 

6 X 366 ir» r 1 J. -1 

77777= TTTT* = 12'5 vv hr per ton-mile. 

367 X 0-48 ^ 



fOO 



<5 



eo 



60 









20 







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— £ 




















- 
























1 











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20 -^ eo eo /oo /£o 

Oudout in Mfrsefifrer 



/■40 



/eo 



Fig. 52. — Curves of Efficiency at Various Outputs for G.E.66A Motors and 

Equipment. 
Curve E. — G.E.66A motor efficiency ^excluding gear). 
Curve F. — G.E.66A motor efficiency (including gear) as determined by factory tests 

at steady load. 
Curve S. — Over-all efficiency of the electrical equipment under actual service 
conditions. 



The total energy for momentum and train-friction thus comes to 
41'0 + 12-5 = 53*5 w hr per ton-mile. If from this amount we 
deduct the 14 w hr per ton-mile supplied by the potential energy of 
altitude, we obtain a remainder of 53"5 — 14*0 = 39*5 w hr per ton- 
mile as that part of the electrical energy obtained from the supply, 
which is ultimately transformed into momentum and into the energy 



CENTRAL LONDON RAILWAY 



91 



of train-friction. Thus, 39"5 w hr per ton-mile constitutes the 
output of the electrical equipment. Measurements of the input to 
the trains {i.e. measurements of the energy consumption) were made 
on trains composed of various numbers of coaches. The following 
study relates to the results obtained with trains of from 7 to 3 
coaches. The particulars of these trains, together with rough 
estimates of the train-friction, are given in Table XXVI 11. The 
weight of the average passenger is taken as 62*5 kg (138 lbs). 
Each motor-coach weighs 23 tons and seats 42 passengers. Each 
trailer-coach weighs 14 tons and seats 48 passengers. 

Table XXVIII. — Analysis of Teain Tests on the Centeal London Rallway. 



Number of coaches per train. 


7 


6 


5 


4 


3 


Number of motor-coaches 


2 


2 


2 


2 


2 


,, of trailer-coaches. 


5 


4 


3 


2 


1 


Total number of seats .... 


324 


276 


228 


180 


132 


Weight of empty train (ton) 


114 


100 


87 


73 


60 


Estimated average number of passengers 












and train staff during test run 


80 


64 


60 


54 


48 


Weight of loaded train (ton) 


119 


104 


91 


77 


63 


Portion of total weight of train allocated to motor- 












coaches, including passengers (ton) 


46 


46 


47 


47 


48 


Ditto to trailer-coaches, including passengers (ton) . 


73 


58 


44 


30 


15 


Added distance allowed for siding opera- 












tions at the two ends of the line (mile) . 


0-48 


0-48 


0-48 


048 


0-48 


Total number of runs which are equivalent 












to a run over the representative section 












(Fig. 50) 


25 


25 


25 


25 


25 


" Equivalent " total distance (mile) . 


12-0 


12-0 


12-0 


12-0 


12-0 


Ton-miles for the round trip 


1,430 


1,250 


1,090 


925 


756 


Total input to train per round trip of 25 












" equivalent " runs (w hr) . 


85,000 


77,700 


67,800 


62,000 


53,200 


Amount deducted for lighting and for the 












compressors of the braking equipment 












(w hr) . 


7,000 


6,000 


5,000 


4,100 


3,100 


Total input required for traction per round 












trip (w hr) . 


78,000 


71,700 


62,900 


57,900 


50,100 


W hr per ton-mile of loaded train 


54-5 


57-4 


57-6 


62-5 


66-2 


Portion allocated to momentum and train- 












friction ...... 


39-5 


39-5 


39-5 


39-5 


39-5 


Portion allocated to losses in the electrical 












equipment ...... 


15-0 


17-9 


18-1 


23-0 


26-7 


Corresponding efficiency of electrical equip- 












ment 


72-5 


68-9 


68-5 


63-2 


59-6 



The gradual decrease in the efficiencies with decreasing numbers 
of trailers is readily understood when we consider that the average 
load on the motors is smaller the less the number of trailers, and 
that the efficiency of the motors falls off rapidly with decreasing load. 
To further elucidate this point, let us carry through the calcula- 
tions shown in Table XXIX. 



92 



ELECTRIC TRAINS 



Table XXIX.— Continued Analysis of Train Tests on the Central 

London Railway. 



Number of coaches per train. 



Number of motor-ooaches .... 
,, of trailer-coach.es 

Weight of loaded train (ton) 

Input to traction equipment per ton-mile 
(w hr) ....... 

Ditto per train-mile (w hr) 

Ditto (kw hr per train per hour) 

Average rate of consumption of electricity 
per train by traction equipment (kw) 

Pressure at train (volts) .... 

Average current supplied to train for traction 
(amperes) . . . . 

Number of motors per train 

Current per motor (amperes) 

Rated output of each motor (hp) 

Efficiency of motor, including gearing at its 
rated load (per cent.) .... 

Current input to motor at its rated load 
(amperes) ...... 

Average current for these tests in per cent, 
of current at rated load of motors . 

Over-all efficiency of traction equipment for 
entire run (per cent.) .... 

Average load on motors taken over entire 
run (kw) ...... 

Ditto (hp) 

Average load per motor (hp) 

Percentage which average output consti- 
tutes of rated load of motor . 

t Average load on each motor in hp, taken 
over the time during which electricity is 
being consumed ..... 

Percentage which this load constitutes of 
rated load ...... 

♦Efficiency of motor alone, from factory 
tests at steady load, for above average load 
while electricity is being consumed 

Ratio of efficiency of motor at factory on 
steady load to efficiency of electrical equip- 
ment in service ..... 



2 

5 

119 

54-5 
6,490 
102 

102 
500 

204 
4 
51-0 
125 

90 

208 

24-5 

72-5 

74-0 
99-1 

24-8 

19-8 

56-8 
45-5 

87-4 

1-20 



2 

4 

104 

57-4 

5,960 

93-7 

93-7 
500 

187 
4 
46-8 
125 

90 

208 

22-5 

690 

64-5 
86-5 
21-6 

17-3 

49-5 
39-6 

86-0 

1-24 



2 

3 

91 

57-6 

5,250 

82-5 

82-5 
500 

166 
4 
41-3 
125 

90 

208 

19-8 

68-4 

56-5 
75-7 
18-9 

15-1 

43-4 
34-7 

84-5 

1-24 



2 
2 

77 

62-5 

4,810 

75-6 

75-6 
600 

151 
4 
37-8 
125 

90 

208 

18-2 

63-2 

47-8 
64-0 
16-0 

12-8 

35-6 
28-5 

82-0 

1-30 



2 

1 

63 

66-2 

4,170 

65'6 

65-6 
500 

131 
4 
32-8 
126 

90 

208 

15-8 

59"6 

39-1 
62-4 
13-1 

10-5 

30-0 
24-0 

79-0 

1-33 



The four 125-hp motors and their control apparatus constitute an 
aggregate equipment of 500 hp for each of the above trains. This 
electrical equipment weighs 9*8 tons. 

With this added data, let us institute a few further comparisons 
in Table XXX. 

* These values are obtained from the Motor Efficiency Curve given in Fig. 52 for 
the values of hp per motor given in Item t- 




Fig. 53. — Outside Elevation of Central London Motor- Coach. 





m 


1 




riLii-iHH-lirl,:i|fi^p| - -1 


1 




1 





Fig. 54. — Outside Elevation of Central London Trailer-Coacli. 




Fig. 55. — Interior View of Central London Trailer-Coach. 

[To /ace p. 92. 



CENTRAL LONDON RAILWAY 



93 



Table XXX. — Continued Analysis of Train Tests on the Centeal 

London Railway. 



Number of coaches per train. 



Weight of loaded train (ton) 
Rated hp per ton weight of train 
Weight of electrical equipment (kg per ton 
weight of train) ..... 



7 


6 


5 


4 


119 
4-20 


104 
4-80 


91 
5-50 


77 
6-50 


82-4 


94-2 


108 


127 



63 
7-98 



155 



This last item, the weight of the electrical equipment per ton 
weight of train, will vary greatly with the service required as regards 
the schedule speed and the number of stops per mile. 

We have seen, in Table XXIX., that for a 6 -coach train operating 
to a schedule speed of 15 '7 ml ph, with a stop every 0*48 mile, the 
average load per motor during these test runs was only 21 "6 hp, which 
is only 17*3 per cent, of the rated output of the motors. In regular 
service, with the less skilful manipulation of the average driver, 
and with the necessity of keeping to the time-table under adverse 
circumstances, such as occasional prolonged stops in discharging and 
embarking passengers, the average load will be from 20 to 25 per 
cent, more of the rated load, instead of the 17*3 per cent, obtaining on 
test. Under these conditions the temperature-rise of the motor after 
its day's work of from 15 to 18 hours* consecutive service, is some 60°. 
The equipments are quite ample for handling 7-coach trains, but the 
traffic appears to be well met with 6-coach trains made up of two 
motor-coaches and four trailers in the busy hours. During the middle 
of the day, 3-coach trains, consisting of one motor-coach and two 
trailers, are sometimes substituted. 

While the schedule speed of 15*7 ml ph has been employed on 
occasions, with a running time of 22 minutes from Shepherd's Bush 
to the Bank, the customary schedule is 14 ml ph, which cor- 
responds to a time of 25 minutes between Shepherd's Bush and the 
Bank. 

Table XXXI. consists of a specification of this Central London 
Railway 6-coach train. Fig. 53 shows a photograph of the motor- 
coach complying with this specification, and Fig. 54 a photograph 
of the trailer-coach. A photograph of the inside of this Central 
London trailer-coach is shown in Fig. 55. 

The Central London Railway now extends beyond Shepherd's 
Bush to Wood Lane, and at the other end it is about to be extended 
beyond the Bank to Liverpool Street. This latter section was 
included in the preliminary scheme for the line, but, for various 
considerations, was not constructed. 



94 



ELECTRIC TRAINS 



Table XXXI.— Specification of a Six-Coach Train on the Genteal London 

Railway. 



A. — Motor-Coach. B. — Trailer-Coach. 0. — Complete Train. 


A. — Motor-Coach. 




General — 




Total length of coach over headstocks .... 


. 45 ft 6 in 


Length of driver's cab (and equipment compartment) 


. 12 ft in 


„ of passenger compartment ..... 


. 30 ft 3 in 


„ of rear platform ...... 


3 ft 3 in 


Length between centres of bogies ..... 


. 29 ft in 


Height, over-all, from rail ...... 


. 9 ft 4J in 


„ of passenger floor above rail .... 


2 ft in 


Width, over-all, outside ....... 


8 ft 6 in 


Seating capacity ........ 


42 


Weight of coach without passengers .... 


23-5 tons 


„ on driving wheels without passengers . 


16*5 tons 


„ on trailing wheels without passengers 


7-0 tons 


„ of coach body, including under-frame, air compressors, 


seats, upholstering and all fittings .... 


12-2 tons 


Seats per foot length of coach 


. 0-92 


„ ton weight of coach ..... 


. 1-79 


Bogie Trucks — 




Weight of motor bogie without motor .... 


3-9 tons 


„ trailing bogie, about ..... 


2-0 tons 


Wheel base of motor bogie ...... 


. 6 ft 


„ of trailing bogie ...... 


. 6ft 


Length over frame of motor bogie ..... 


9 ft 6 in 


„ inside frame of motor bogie .... 


. 8 ft 10 in 


Width over frame „ » 


6 ft 6 in 


„ inside frame ,» „ .... 


. 5 ft 10 in 


Gauge of track ........ 


. 4 ft 8i in 


Weight sustained per motor axle (unloaded coach) . 


8-3 tons 


Ditto (portion which is spring supported) .... 
Ditto (portion which is direct supported) .... 


6-3 tons 


2-0 tons 


Weight sustained per trailing axle (unloaded coach) 


3*5 tons 


Ditto (portion which is spring supported), about 


3-0 tons 


Ditto (portion which is direct supported), about 


0-5 tons 


Diameter of driving wheels (with new tyres) .... 


2 ft 11 in 


„ of trailing wheels ( „ » ) • 


2 ft 5 in 


Axle diameter (motor bogie) mid frame ..... 


5 in 


„ „ „ at hub . • . . . 


6 in 


„ ,„ „ at gear wheel seat 


6 in 


„ „ n at journals . . . , . 


. 4|in 


Electrical Equipment — 




Type of motor ......... 


G.E.66A 


Rated hp ......... . 


125 


Pressure in volts 


500 


Efficiency (per cent.) full load ...... 


90 


,, ,, ? j» ...... 


90 


1 

>> >> 2 »> ...... 


88 


1 
,, ,, 4 >> ...... 


80 



The method of control is by the Multiple Unit System, there being two motor- 
coaches per train. The electrical equipment is carried at the two ends of the train. 
The contactors and rheostats are placed in a steel compartment (behind the driver's 
cab) which is separated from the passenger compartment by a steel bulkhead and a 
lining of asbestos. 



CENTRAL LONDON RAILWAY 



95 



Particulars of gear on motor- 
Cast steel spur wheel 

Mild steel pinion 

Ratio .... 

Weight (with case), about 
Weight of one motor alone 
Weight of one motor and gear 
Motors per motor-coach (and per motor bogie) 
Total weight of motors with gearing per motor-coach 
Weight of balance of electrical equipment {i.e. controllers, 

contactors, rheostats, etc.) per motor-coach 
Total weight of electrical equipment per motor-coach 
Ratio of total weight of electrical equipment to weight of motors 
and gearing .......... 

Weight of motor in kg per hp (rated) ...... 

,, ,, and gear in kg per hp (rated) .... 

„ of motors and gearing in kg per ton weight of motor-coach . 

,, of all electrical equipment in kg per ton weight of motor-coach 
Ratio of total weight of electrical equipment to total weight of motor- 
coach ........... 



69 teeth 

15 teeth 

. 3-94 

210 kg 

1'75 tons 

1-96 tons 

2 

3-92 tons 

1-0 

4-92 tons 



1-26 
14-2 
15-9 
167 
210 



0-21 



B. — Teailer-Coach. 



Total length of coach over headstocks 

Length of passenger compartment . 
,, of rear platforms, each 
,, between centres of bogies 

Height, over-all, from rail 
„ of floor above rail 

Width, over-all, outside 

Wheel base of bogies 

Seating capacity . 

Weight of coach without passengers 

Seats per foot length of coach 
,, ton weight of coach 



46 ft 6 in 
. 39 ft 
3 ft 3 in 

29 ft 6 in 

9 ft 4J in 

2 ft in 

8 ft 6 in 

5 ft in 

48 

13*5 tons 

. 1-06 
. 3-56 



t 



The doorways are 2 ft 10 in wide, and are situated at the ends of the passenger 
compartments. 

C. — Complete 100-Ton, 6-Coach Tbain. 

Number of motor-coaches 

„ of trailer-coaches 
Total length . 
Weight of motor-coach component 

,, of trailer-coach ,, 

Total weight of 6-coach train 

,, seating capacity . 
Number of motors on train . 
Total hp per train (rated) 
Weight of motors and gearing per train 
Total weight of electrial equipment 

Seats per foot length of train 

,, ton weight of train 
Rated hp per ton of train 

,, „ seat of train . 

Total weight of motors and gearing in kg per ton weight of train 

„ „ electrical equipment in kg per ton weight of train 

Ratio of total weight of electrical equipment to total weight of train 0*098 

The braking equipment consists of Westinghouse Automatic Brakes, for which 
motor-driven compressors and the necessary brake gear are provided beneath the 
coaches. 



2 


4 


. 276 ft 


47 tons 


54 tons 


101 tons 


276 


4 


500 


7-84 tons 


9-8 tons 


1-00 


. 2-73 


. 4-95 


. 1-81 


78 


98 



96 ELECTRIC TRAINS 



Examples. 

1. A railway line has its profile similar to Fig. 50, but with a vertical fall of 4 m, 
and a distance between stations of 0*68 mile (1290 m). A train is run over the 
line at a schedule speed of 20 ml ph. Estimate the actual train consumption. 

Ans. 84 w hr per ton-mile (100 w hr per ton-mile on level track). 

2. From Table XXVIII. plot the values of the energy input (w hr per ton- 
mile) as ordinates against train weights as abscissae, and notice the marked decrease 
in train consumption per ton-mile with increased train weight. 

3. As determined from the speed-time diagram for a schedule speed of 25 
ml ph and 1*2 mile between stops, the input for momentum and friction was 64 
w hr per ton. 

Mean acceleration and deceleration was 1*5 ml phps. 
Estimate (a) Probable input per ton-mile. 
(&) Average input per ton. 

Ans. (a) 75 w hr per ton-mile. 
(6) 1-88 kw per ton. 

4. A train weighing 130 tons is to run to a schedule of 20 ml ph, 0*6 mile 
between stops, (a) What motors should be installed ? (b) If the electricity is 
supplied for two-thirds of the distance, and train friction is 6 kg per ton, estimate 
the crest speed to be attained during each run if the efficiency of the equipment 
is 67 per cent. 

Ans. {a) Eight 160-hp motors. 
(5) 33-5 ml ph. 



CHAPTER VII 

ANALYSIS OF SOME ENERGY CONSUMPTION TESTS OF 
TRAINS ON THE GREAT NORTHERN PICCADILLY AND 
BROMPTON RAILWAY 

The tests described in this chapter were made in March, 1907, on a 
train consisting of one motor-coach and three trailer-coaches. Each 
motor-coach weighed 27*5 tons, and each trailer weighed 16*5 tons, 
the weight of train, exclusive of passengers, thus aggregating 77 tons. 
The weight of the passengers on the train during these tests was 
estimated to average 3 tons, bringing up the weight of train, 
inclusive of passengers, to 80 tons. 

The train was run over the whole route, and the energy consumed 
at the train was recorded at each stop. The entire distance between 
the termini at Hammersmith and Finsbury Park is 8*9 miles, and 
comprises 20 runs between stations. Thus, M, the average distance 
from start to stop, is — 

8'9 

^ = 0*445 mile. 

Two tests, A and B, were carried out. Each comprised two runs 
between termini, in opposite directions, and the average value of the 
schedule speeds in both directions was — 

For Test A . . . 14-56 ml ph. ' 
„ B . . . 15-43 „ 

The average duration of stops at stations was 12 seconds. The 
running time between termini was — 

For Test A : :r|^ X 3600 = 2200 seconds. 
14*5d 

„ B: ^x 3600 = 2075 „ 

The 19 intermediate stops occupied an aggregate of — 

19 X 12 = 228 seconds. 

97 H 



98 



ELECTRIC TRAINS 



Consequently, the total time during which the train was in motion 
was — 

For Test A . . . 2200 - 228 = 1972 seconds. 



B 



2075 - 228 = 1847 



This gives for value of T, the time occupied by the average run from 

start to stop — 

1 Q72 
For Test A =^ = 98*6 seconds. 



B 



20 

1847 
20 



= 92-4 



The average speed from start to stop is — 

^ rv ^ A 98-6 + 12 ,,_ 110-6 X 14-56 _^ , , 
For Test A : — 7<^ — X 14-56 = 7^7^^ = 16*3 ml ph. 



B 



98-6 

92-4 + 12 

92-4 



X 15-43 = 



98-6 

104-4 X 15-43 

92-4 



= 17-5 ml ph. 



The average time during which electricity was supplied to the 
train was — 

For Test A . . .41 seconds. 

„ B . . . 44 „ 

The maximum speeds were not recorded, but the two speed-time 
diagrams shown in Fig. 56 may reasonably be taken as approximating 

X 



-is 

4 



/o 







































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Currt 


A 


B 


















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J 


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// 


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\ 














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\ 


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i 


' 


































\ 


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V 






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& 









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Time in 3e.concls 



Fig. 56.— Average Speed-time Diagrams for Great Northern Piccadilly and 
Brompton Eailway Tests A and B, from Values in Table XXXII. 



PICCADILLY TUBE RAILWAY 



99 



to the average conditions for these runs. From these speed-time 
diagrams we obtain — 



For Test A 
B 



maximum speed = 22*5 ml ph. 
= 25-0 ml ph. 



The altitude of the line at Finsbury Park is considerably greater 
than at Hammersmith ; but by averaging the energy consumption 
in both directions, a rough approximation to the conditions of a level 
run is obtained. The average results for Tests A and B are set forth 
in Table XXXII. on the following page. 

The longest run between stops is the 0*99 mile between Baron's 
Court and Earl's Court. The shortest is the 0'18 mile between 
Leicester Square and Covent Garden. The average distance between 
stops over the entire route is, as already stated, 0*45 mile. It is 
instructive to compare the results for these three cases, averaged over 
the two directions, to eliminate grades so far as practicable. The 
three distances are 0*18 mile, 0*45 mile, and 0*99 mile. The average 
speeds from start to stop are 12*7 ml ph, 16*9 ml ph, and 20*8 ml ph. 
The amounts of energy consumed at the train work out at 121 
w hr per ton-mile, 78 w hr per ton-mile, and 59 w hr per ton-mile. 
Taking the duration of each stop at 12 sec, the corresponding 
schedule speeds are 10*2 ml ph, 15*0 ml ph, and 19*5 ml ph. Thus 
we have the following summary : — 



Distance between stops (mile). 


Schedule speed (ml ph). 


Energy consumption (w hr per 
ton-mile). 


0-18 
0-45 
0-99 


10-2 
15-0 
19-5 


121 
78 
59 



Although the schedule speed in the last case (i.e. the 0*99 mile 
run) is practically twice as great as in the first case (i,e. the 0*18 mile 
run), the energy consumption per ton-mile is only half as great. 
This is a striking example of the influence of the number of stops, 
which are 6 per mile in the first case and just about 1 per mile in 
the last. 



100 



ELECTRIC TRAINS 



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PICCADILLY TUBE RAILWAY 



lOI 



Forty-nine per cent, of the run over this line is on curves, and 
for this reason the estimates of the train-friction loss are based on 
a tractive resistance of 8 kg per ton.* 

With these data the calculations of Table XXXIII. may be 
made — 

Table XXXIII. — Analysis of Teain Tests on the Great Northern 
Piccadilly and Brompton Eailway. 



Designation of Test. 



Mean length of run between stations (mile) 
Duration of stop (seconds) 
Time from start to stop (seconds) 

,, electricity is supplied (seconds) 
Average speed (ml ph) 
Schedule „ „ 

Input for traction (w hr per ton-mile) 
Weight of train, including passengers (tons 
Input for traction (w hr per train-mile) 
Kw hr per hr, i.e. average kvv input . 
Number of motors per train 
Average kw input per motor 

Maximum speed (ml ph), from Fig. 56 . - . 
Momentum energy per ton = 0-0278 x 1*09 x V (w hr) 
Ditto (w hr per ton-mile) . 

Train-friction (kg per ton) 

Mean speed during time electricity is supplied (ml ph) 
Distance covered during this period (m) .... 

Train-friction energy during this period (w hr per ton) 

„ „ „ (w hr per ton-mile) 

Output for momentum and train-friction (w hr per ton-mile) 
Residue of input to ascribe to losses in the electrical equipment 
(w hr per ton-mile) ....... 

Resulting over-all efficiency of the electrical equipment 
Average kw output per motor (from kw input and efficiency) 

,) hp „ „ (from kw output) . 

„ hp „ „ in per cent, of rated output of motor 
(200 hp) 

„ hp output of motor during time electricity is supplied 

Percentage which this load constitutes of rated load . 

Efficiency of the motor on factory test at this load, from Fig. 57 . 

Ratio of factory test efficiency of motor to over-all efficiency of 

electrical equipment ........ 



0-445 
12 
98-6 
41 

16-3 
14-56 
72-4 

80 
5790 
84-4 
2 
42-2 
22-5 
15-3 
34-4 
8 
14-6 

267 

5-81 
130 
47-4 

25-0 
65-5 
27-6 
37-0 

18-5 
100 
50-0 

89-2 

1-36 



0-445 
12 
92-4 

44 
17-5 
15-43 
84-2 

80 
6740 
104 
2 
52-0 
25-0 
18-9 
42-5 

8 
16-2 
318 
6-94 
15-6 
68-1 

26-1 
69-0 

35-8 
48-0 

24-0 
114 
57-0 
89-5 

1-30 



In Fig. 57 is plotted the efficiency curve (including gearing) 
of this motor when operated from a 500-volt circuit under the 
conditions of the manufacturer's tests at the works. Below the 
curve are the points corresponding to the efficiency of the electrical 
equipment as estimated from tests A and B as above described. 



* The subject of the influence of curves on the tractive efiort, is briefly stated 
in Chapter IX. 



102 



ELECTRIC TRAINS 



The motors used on the trains tested are of the G.E.69B type, 
and their weights are given in the detailed specification of the trains, 



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Fig. 57.— Efaciency Curve for G.E.69B Kailway Motor, 500 volt, 200 hp, as used 
on Great Northern Piccadilly and Brompton Kailway. 

compiled in Table XXXIV. A photograph of the outside of the 
trailer-coach is shown in Eig. 58, and the general appearance of the 
inside of the coach is shown in Fig. 59. 



Table XXXIV.— Specification op Six and Foue-coach Trains on Great 
Northern Piccadilly and Brompton Railway. 



A. — Motor-coach. 



B. — Trailer-coach. C. — Complete Train (01, Six-coach; G2, 
Four-coach). 



A.— Motor-Coach. 



General — 

Length of coach, over-all 

,, of coach, over platforms 1 . 

„ of driver's cab (and equipment compartment) 

„ of passenger compartment . 

,, of rear platform ■ 

„ between centre of bogies 
Height, over-all, from rail 

,, of passenger floor above rail 
Width, overall, outside . 
Seating capacity .... 
Weight of coach without passengers 

„ „ body including under-frame, air compressors 

seats, upholstering and all fittings 



Seats per foot length of coach 
,, ton weight of coach 



. 50 ft 

. 49 ft 

13 ft 8 in 

31 ft 6 in 

■3 ft 8 in 

. 33 ft 

9 ft 61 in 

1 ft 11 in 

8 ft 8^ in 

46 

27-5 tons 



12-4 tons 



0-92 
1-67 



PICCADILLY TUBE RAILWAY 



103 



Bogies and Trucks — 

Weight of trailing bogie, about 
Wheel base of motor bogie 

,, of trailing bogie . 
Motor bogie, length over frame 
„ length inside frame 

„ width over frame 

,, width inside frame 

Trailing bogie, length over frame 
„ width over frame 

,, width inside frame 

Gauge of track 

Diameter of driving wheels . 
,, of trailing wheels . 



. 3 tons 
6 ft 6 in 

5 ft in 
) ft 101 in 

9 ft 6 in 

6 ft 9 in 
6 ft in 
8 ft in 
6 ft 6 in 
5 ft 9 in 

4 ft 8^ in 
3 ft 6 in 
2 ft 6 in 



Electrical Equipment — 

Type of motor G.E.69B 

Kated horse-power ........ 200-240 

The manufacturer's usual rating is 200 hp, but on the generally accepted rating 
for railway motors, i.e. 1 hour, 75° C. basis, the motor develops 240 hp. 

Pressure in volts ..... 
Efficiency, full load (200 hp) in per cent. 



500 
88-0 
89-0 
89-2 
82-0 



Method of control is by B.T.H. Multiple-Unit System, there being two motor- 
coaches in the six-coach train, and sometimes one and sometimes two in the four- 
coach train. The contactors and rheostats are placed in a steel compartment (behind 
the driver's cab). 



Gear ratio 32 

Weight (with gear case), about 270 kg 

,, of one motor alone ....... 2-51 tons 

,, of one motor and gear ...... 2*80 tons 

Motors per motor-coach (and per motor bogie) .... 2 

Total weight of motors and gearing per motor-coach . . 6-60 tons 
Weight of balance of electrical equipment {i.e. controllers, 

contactors, rheostats, etc.) per motor-coach 
Total weight of electrical equipment per motor-coach 
Ratio of total weight of electrical equipment to weight of 
motors and gearing ....... 

Weight of motor in kg per hp (200-hp rating) 
„ „ „ „ (240-hp rating) 
„ ,, and gear in kg per hp (200-hp rating) . 
„ „ „ „ „ (240-hp rating) . 
,, of motors and gearing in kg per ton weight of motor-coach 
,, of all electrical equipment in kg per ton weight of motor-coach 
Ratio of total weight of electrical equipment to total weight of motor- 
coach 0*27 



1-68 tons 
7-28 tons 



1-3 

12-7 
10-6 
14-2 
11-8 
207 
270 



B. — Trailee-Coach. 
Length, over-all .... 

,, of coach, over platforms . 

, , of passenger compartment 

„ of rear platforms 

,, between centres of bogies 
Height, over-all, from rail . 

,, of floor above rail . 
Width, over-all, outside 
Wheel base of trucks . 



50 ft 

49 ft 

41ft 

3 ft 8 in 

33 ft 

9 ft 6^ in 

1 ft 11 in 

8 ft 8^ in 

5 ft in 



104 



ELECTRIC TRAINS 



Weight of trucks (two) 

„ of body .... 
Seating capacity .... 
Weight of coach without passengers 

Seats per foot length of coach 
„ ton weight of coach 



5*9 tons 

10-3 tons 

52 

16-2 tons 

1-04 
3-20 



01.— Complete Six-Coach Train. 

Number of motor-coaches . . . . . . . . .2 

,, of trailer-coaches ......... 4 

Total length of train 300 ft 

Weight of motor-coach component . . . . . .65 tons 

„ of trailer-coach „ ...... 65 tons 

Total weight of train . . . . . . . , 120 tons 

,, seating capacity 300 

Number of motors on train d 

Total hp per train (motors, 200-hp rating) 800 

„ ,, (motors, 24:0-hp rating) ..... 960 

Weight of motors and gearing per train .... 11*2 tons 

Total weight of electrical equipment ..... 14*6 tons 

Seats per foot length of train . . . . . . . 1*0 

,, ton weight of train ....... 2*5 

Bated hp per ton of train (motors, 200-hp rating) . , . 6*66 

„ „ „ (motors, 240-hp rating) ... 8-0 

Rated hp per seat of train (motors, 200-hp rating) . . . 2*66 

„ „ „ (motors, 240-hp rating) . . . 3*20 

Total weight of motors and gearing in kg per ton of train . . 94-7 

„ „ of electrical equipment in kg per ton of train . . 122 

Ratio of total weight of electrical equipment to total weight of train 0*122 

The six-coach train is capable of division into two three-coach trains, which will 
have the same proportional values per ton and per seat of train as above. Extra 
master controllers are fitted on the centre trailer-coaches for use when divided into 
three-coach trains. Many of these three-coach (divided) trains are used during light- 
service hours, also some four-coach trains (two motor-coaches and two trailer-coaches). 

C2. — Complete Four-Coach Train. 

Number of motor-coaches 
Number of trailer-coaches 
Total length .... 

Weight of motor-coach component 
Weight of trailer-coach component 
Total weight of train . 
Total seating capacity . 
Number of motors per train . 
Total hp per train (motors, 200-hp rating) 
„ „ (motors, 240-hp rating 

Weight of motors and gearing per train 
Total weight of electrical equipment 

Seats per foot length of train 
Seats per ton weight of train 
Rated hp per ton of train (motors, 200-hp rating) 
„ „ „ (motors, 240-hp rating) 

Rated hp per seat of train (motors, 200-hp rating) 
„ „ „ (motors, 240-hp rating) 

. Total weight of motors and gearing in kg per ton 
of train ..... 
Total weight of electrical equipment in kg per ton 

of train ..... 
Ratio of total weight of electrical equipment to total 
weight of train 



1 


2 


3 


2 


200 ft 


200 ft 


27-5 tons 


55 tons 


49 tons 


32*5 tons 


76-6 


87*5 tons 


202 


196 


2 


4 


400 


800 


480 


960 


5*6 tons 


11-2 tons 


7-3 tons 


14*6 tons 


1*01 


0*98 


2*64 


2*24 


5-2 


9-2 


6*3 


11*0 


2*0 


4*1 


2-4 


4-9 


74*4 


130 


96*8 


169 


0*097 


0*169 




Fig. 58. — Outside Elevation of Great Northern Piccadilly and Bronipton 

Railway Trailer-Coacli. 




Fig. 59. — Interior View of Great Northern Piccadilly and Bronipton 

Railway Trailer-Coach. 



[Tofaci'p. 104. 



PICCADILLY TUBE RAILWAY 



105 



The reader will not have failed to notice that not only in this 
G.N.P. and B. train, but also in the C.L.E. trains, and in the 
L. and Y. trains, the efficiency of the electrical equipment is higher, 
the greater the percentage of rated load carried by the motors during 
the time that electricity is being consumed from the line, to supply 
the electrical equipment on the train. In Fig. 60 the results already 
given of efficiency estimates for these three railways are brought 
together. The two results represented by small squares relate to 
the G.N.P. and B. tests which we have just analysed in this 




00 



Jircentage rrhich jirer^^ Load qf Motor trhiJe die ^/tcCnc/dy is on, 
constitutes q/ Che /fated Load of the A7o£or 

Fig. 60.— Grouping of the Over-all Efficiencies of Electrical Equipment for L. and 
Y.B., C.L.R., and G.N.P. and B.R., from Chapters V., VI. and YII. 



chapter. But for these two points the motors are taken at the 
rating of 200 hp for which they are sold. It is, however, well 
known that these motors rate at 240 hp when referred to the 
1-hour, 75° C. basis. The data given in Table XXXV. shows 
that on this latter rating, the average loads in the two cases 
were 41*6 per cent, and 47*5 per cent, of the (1-hour, 75° C.) rated 
load. 

The two results indicated by the two crosses in Fig. 60 represent 
the values in the last column of Table XXXV. The L. and Y. 
results of Chapter V. are indicated by the two triangles, and the 
C.L.E. results of Chapter VI. are indicated by the cii'cles, the double 
circle representing the normal 6-coach train. 



io6 



ELECTRIC TRAINS 



Table XXXV.— Showing the Loading of the Great Northern Piccadilly 
AND Brompton Railway's Motors during the Tests A and B op Table 
XXXIII. 



Average load in hp 
while electricity 


Over-all efficiency of 

equipment in actual 

service. 


Percentage which A is of rated load when 
the rating is taken as — 


is on. — A. 


200 hp. 


240 hp. 


100 
114 


65-5 
690 


500 
57-0 


41-6 

47-5 



We thus see that, far from being contradictory, the results 
obtained on these different tests on three different railways, are in 
remarkable agreement, considering the inevitably rough practical 
nature of such tests on the road. 

We may, with considerable assurance, take the curve drawn in 
Fig. 60 amongst these points, to be fairly representative of modern 
equipments of series-wound, continuous-electricity railway motors. 
This curve teaches us the important lesson that there is a better 
reason than saving in weight, for advocating the application of forced 
draught to continuous equipments, since we could operate smaller 
motors at a much higher average load, and with a considerable 
improvement in the over-all efficiency of the equipment. With 
the excellent commutation attainable with modern interpole motors, 
the plan should be very practicable, since, even at the high over- 
loads encountered during the accelerating period, excellent com- 
mutation may be relied upon. 

Mr. J. E. Chapman, Chief Engineer of the Underground 
Electric Eailways Co. of London, has supplied the author with some 
valuable data bearing on the question of the most economical 
schedule speed. The data applies to the Great Northern Piccadilly 
and Brompton Eailway. From March 11 to April 29, 1907, the 
trains on this railway were operated to a schedule speed of 14*82 
ml ph. From April 29 to October 14, 1907, the schedule speed was 
15*24 ml ph, and after October 14, 1907, the schedule speed was 
16*1 ml ph. 

The following results are not in the form in which they were 
supplied to me, but are so arranged as to better supplement the 
earlier data in this chapter. The calculations involve certain 
assumptions which must, however, be closely correct. 



PICCADILLY TUBE RAILWAY 



107 



Designation of service. 


I. 


II. 


III. 


Schedule speed (ml ph). .... 


14-8 


15-2 


161 


Single-trip time (minutes) .... 


36 


35 


33 


Average number of coaches per train 


3-30 


3-17 


4-00 


Estimated average weight of train, with passen- 








gers (tons) ...... 


67 


65 


80 


Number of motor-coaches per train 


1 


1 


1 


Consumption per ton-mile (from data supplied) 








(w hr) 


67-0 


78-0 


88-7 


Train-miles per week ..... 


39,000 


39,000 


42,500 


Consumption per train-mile (kw hr) 


4-50 


5-06 


7-10 


Consumption per week (kw hr) . . . 


176,000 


198,000 


302,000 


Consumption reduced to reference basis of 








40,000 train-miles per week 


180,000 


203,000 


284,000 


Further reduced to reference basis of 70-ton 








trains 


188,000 


218,000 


248,000 


Cost of electricity per week (taken at Id. per 








kw hr) . 


£785 


£910 


£1035 



With the 16*1 ml ph service, two less trains are required to 
provide the aggregate of 40,000 train-miles per week, than are 
required for the 14*8 ml ph service. Thus, from the (£1035 — 
£785 = )£250 per week greater cost for electricity, is to be deducted 
the cost of working two trains and the capital charges associated 
with them. It should also be remembered that the faster service 
constitutes a feature calculated to attract an increased number of 
passengers. This leads to a greater percentage of seats occupied. 
Furthermore, it is better to work a train at high speed, realize its 
earnings, scrap it after it has done its reasonable mileage and buy a 
new train, than spare it to the extent of spreading out over a greater 
term of years its total earning capacity. The former plan will 
obviously yield a greater return for a given amount of capital invested 
in rolling stock. 



CHAPTER VIII 

ACCELERATION AND TRACTIVE FORCE 

The acceleration due to gravity is usually denoted by the letter g. 
When expressed in meters per second per second (m psps) we 
have — 

g = 9-81. 

But 1 m psps is equal to 2*24 ml phps. Consequently, when 
accelerations are expressed in ml phps, we have, for the acceleration 
due to gravity — 

g = 9-81 X 2-24 = 220. 
We also have the relation — 

Y =— X a 
9 

for the tractive force required to accelerate at the rate a, a body of 

weight W when moving in a frictionless medium. Consequently, if 

a, the acceleration, is expressed in ml phps, and if the body weighs 

1 ton {i.e. if W = I'OO), then, for the tractive force in tons per ton, 

we have the expression — 

220 • 
For an acceleration of 1 ml phps, we have — 

F = fr^y^ = 0455 ton per ton of weight accelerated. 

= 45*5 kg per ton of weight accelerated. 

While the entire train is being accelerated, producing a cor- 
responding increase in its translational momentum, certain parts — 
the wheels, axles and motor armatures — are gathering rotational 
momentum, and will need a corresponding amount of energy to 
provide such momentum. 

This point was considered in Chapter IV., where an additional 
9 per cent, was added to the translational energy to give the total 

io8 



ACCELERATION AND TRACTIVE FORCE 109 

energy (i.e. including the rotational component). The same allow- 
ance should be made here, and, therefore, when accelerating at 1 
m phps, the figure of 45*5 kg per ton of material accelerated becomes 
49 '5 kg per ton of train accelerated. 

Thus, we have the simple rule that when a train is being accele- 
rated, the component of the total tractive force required to provide 
the momentum (i.e. exclusive of the component required to overcome 
train-friction) is, per ton weight of train, and per ml phps of 
acceleration, equal to 49*5 kg. 

Thus, if a train weighs 70 tons, and if it is desired to bring it up 
to its crest speed, with an average acceleration of 0'90 ml phps, 
then the average tractive force during the accelerating period 
(exclusive of the amount required to overcome train-friction), is 
equal to — 

49-5 X 70 X 0-90 = 3120 kg, 

or 3'12 tons. If the average value of the train-friction during this 
period is 6 kg per ton, then the average tractive force required to 
overcome train-friction is equal to — 

6 X 70 = 420 kg, 

or 0*42 ton. Consequently, in this case, the average value of the 
total tractive force is equal to — 

3-12 -I- 0-42 = 3-54 tons. 

The average tractive force per ton is made up of-— 

49*5 X 0*90 = 44*5 kg per ton for acceleration, and 
6*0 kg per ton for friction, 

resulting in a value for the average tractive force of — 

44-5 -I- 6-0 = 50-5 kg per ton, 

or a total tractive force of (0*0505 X 70 =)3'54 tons for the 70-ton 
train. 

In Fig. 61 is given a speed-time diagram for a run of 0*48 mile 
from start to stop. The run is accomplished in 95 seconds. Con- 
sequently, the average speed is — 

?|^ X 0-48 = 18-2 ml ph. 

After 48 seconds from the start the train has attained its crest 
speed of 25*5 ml ph. Consequently, the average acceleration during 
these 48 seconds is — 

— —- = 0*53 ml phps. 
48 ^ ^ 

The acceleration is, however, varying during these 48 seconds. 



no 



ELECTRIC TRAINS 



At any given instant it is equal to the rate of change of speed at 
that instant. Taken over any very short interval of time, the curve 
is approximately straight. Thus, over the short portion extending 
from a speed of 14 ml ph to a speed of 16 ml ph, we may take it 
as a straight line. By drawing the small triangle indicated in Eig. 
61 we see that the change of 2 ml ph in the speed (i.e. the change 
of from 14 to 16 ml ph) occupies 2*7 seconds, for the speed is seen to 
be 14 ml ph 14*8 seconds after the start, and it is 16 ml ph after 17*5 



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<s 


V 






X 


V 





7^/>70 in Seconde 

Fig. 61. — Determination of Acceleration and Power from Speed-time Diagram. 

seconds from the start. The average acceleration corresponding to 
the mean speed of — 

ii+li^ = 15 ml ph 

is consequently — 

16-14 2-0 ^^, , ^ 
j^:^^:3j;g = 2;^=0-74mlphps. 

If we extend the hypotenuse of this little triangle, we obtain 
a tangent to the curve at the point corresponding to a speed of 15 
ml ph and to — 

j: = 162 seconds 

from the start. By measuring the slope of this tangent in the scale 
of the axes, we obtain (see the large triangle)— 

22-4 - 8-0 14-4 ^ ^o 1 1. 
WV^Wl = 19^ = ^'^^ ^^ P^P'- 



ACCELERATION AND TRACTIVE FORCE iii 

(The base of this triangle may be conveniently arranged to 

measure an even figure — say 20 in this case — the result being, of 

,, 21-6 - 7-0 ^.^.^ . 
course, the same, ^ = O'lo.) 

From the construction it is obvious that the result is necessarily 
the same as that obtained by the first calculation for the small triangle. 
Owing to the greater length of the hypotenuse, and the greater accuracy 
thereby obtained in the readings, the method of determining the 
acceleration at any point of the curve by drawing a tangent to the 
curve, and passing through that point, is the most useful and accurate 
graphical construction by means of which to calculate the acceleration. 



/.O 








/• 


\ 
















- 




J 


/ 


\ 




















/ 




\ 


















































\c 






















/ 




s 


V 
















it 


/ 




\ 


\^ 


V 














f 








> 


^ 

V 


\ 


x_ 








i 


f 










\ 


V 


^^ 


^ 




















^ 


V, 


^ 






1 

























dooo 






tooo 



20 
7?/ne }n sec. 



40 



60 



Fig. 62. — Acceleration and Power Curves deduced from the Speed-time Diagram 

in Fig. 61. 



Otherwise expressed, we may say that the acceleration corresponding 
to any point of the speed-time diagram is proportional to the slope of 
the tangent to the curve at that point (the slope being the ratio 
of the vertical and horizontal distances between two points on the 
tangent, both distances being measured to the scales of the corre- 
sponding axes). Thus, the steeper the curve at any point, the greater 
the corresponding acceleration or deceleration, as the case may be. 

In Fig. 62 the upper curve represents the values of the accelera- 
tion for the first 48 seconds of the diagram in Fig. 61. 

It has been obtained by drawing lines tangent to the speed- time 



112 



ELECTRIC TRAINS 



diagram at each successive 5 seconds from the start. The values of 
the slopes (i.e. the values of the ratio of the increment in speed to 
the corresponding increment in time) are equal to the values of the 
corresponding acceleration. Thus, referring again to Fig. 61, we see 
that the speed of 15 ml ph, for which we obtained 0*73 for the 
value of the corresponding acceleration, occurred 16*2 seconds after 
the instant of starting from rest, and, turning to the upper curve in 
Fig. 62, we find that, corresponding to an abscissa of 16*2 seconds, 
the value plotted for the acceleration is 0*73 ml phps. Further- 
more, if we obtain the mean ordinate of this acceleration curve for 
the 48 seconds which elapse from the start up to the crest speed of 
25*5 ml ph, we find it to be 0*53 ml phps, which, as we have 
already seen, is equal to the crest speed (25*5 ml ph) divided by 
the time (48 seconds) elapsing while this speed was being acquired. 
From this acceleration curve we could construct a curve showing 
the corresponding values of the tractive force per ton, by the rule 
that an acceleration of 1 ml phps requires (neglecting friction) a 
tractive force of 49*5 kg per ton, and by adding a further 6 kg per 
ton for the tractive force required to overcome friction. This portion 
of the calculation can, however, be well worked out tabularly, as in 
Table XXXVI.— 

Table X^^XVI. — Calculations of the Power Curve for the Speed-time 
Diagram indicated in Fig. 61. 



Interval 


Mean 

accelerat- 
ing rate 
during 
interval 

(ml phps). 


Tractive force 
(kg per ton). 


Total 

tractive 

force (kg 

per ton). 


Mean 

speed 

during 

interval 

(ml ph). 


Mean 
speed in 
meters 
per sec. 
(0-447 X 
speed in 
ml ph). 


Power 

per ton 

(kg m per 

sec). 


Power 


(seconds). 


For ac- 
celeration. 


For 
friction. 


(watts). 


0-5 
5-10 
10-15 
15-20 
20-25 
25-30 
30-35 
35-40 
40-45 
45-48 


0-90 
0-99 
0-93 
0'70 
0-54 
0-41 
0-30 
0'22 
0-15 
0-12 


44-5 
49-0 
46-0 
34-6 
26-7 
20-3 
14-8 
10-9 
7-4 
6-0 


6'0 
60 
6-0 
60 
60 
6-0 
6-0 
6-0 
6-0 
6-0 


50-6 
65-0 
52*0 
40-6 
32-7 
26-3 
20-8 
16-9 
13-4 
12-0 


2'6 
6-8 
12-0 
16'0 
19-0 
21-2 
22-8 
24-0 
24-7 
25-4 


1-16 

3-04 

5-37 

7-15 

8-50 

9-50 

10-20 

10-73 

11-05 

11-35 


59 
167 
279 
290 
278 
250 
212 
181 
148 
136 


680 
1640 
2740 
2840 
2730 
2450 
2080 
1780 
1450 
1330 



By multiplying the total tractive force (kg) at any instant by 
the speed in m ps at that instant, we obtain values of the power 
in kg m ps. Now, since — 

1 kg m ps = 9 81 watts, 



ACCELERATION AND TRACTIVE FORCE 113 

we can obtain the power in watts by multiplying the above values 
for kg by 9-81. 

The figures in the last column, which are plotted in the lower 
curve in Fig. 62, represent tlie power delivered by the motors to 
the axles of the train. The average value is 1960 watts, while the 
maximum value is 2840 watts, or 45 per cent, greater than the 
average. These figures relate to the 48 seconds during which 
the train is drawing electricity from the line. The time from start 
to start is, however — 

95 + 15 = 110 seconds. 

Consequently, the average power required at the axles over the whole 
run is — 

48 

— p^ X I960 = 855 watts per ton. 

The ratio of the maximum value to this average value for the entire 
run is 3*3. 

All these figures have related to the output from the electrical 
equipment. To change from power to energy, let us write down the 
855 watts per ton as 855 w hr per ton per hour. Now, since the 
schedule speed is 15*7 ml ph,* the average output of the motors is — 

855 

:--^j-^ = 54*5 w hr per ton-mile. 

15'7 

Working this out by our earlier methods of adding together the 
energy required for momentum and friction, we arrived at the result 
of 53"5 w hr per ton-mile (see Chapter VI. p. 90). The discrepancy 
(of 2 per cent.) is very slight, and is due to taking averages of 
ordinates separated from one another by so great an interval as 
5 seconds, and also to errors in deriving by graphical methods the 
acceleration curve from the speed-time diagram. 

It may, in general, be said that the subject is best approached 
from the standpoint discussed in the previous chapters, when the 
object is to estimate the input in w hr per ton-mile, and from this 
acceleration-curve standpoint, when studying the instantaneous values 
of the power required. 

In general practice it will be found that trains are equipped with 
sufficient motor capacity to ensure that the average load, taken over 
the entire journey, shall be only some 20 to 25 per cent, of the rated 
load on the 1-hour, 75° basis of rating. Taking such a case as that 
which we have just investigated, and assuming that it is desired that 

* The speed-time diagram of Fig. 61 is reproduced from Fig. 51 of Chapter VI., 
where it will be found that the duration of stops is 15 seconds and the schedule 
speed 15-7 ml ph. 



114 ELECTRIC TRAINS 

the motors' average load shall be only 25 per cent, of their rated load, 
then we find that the motors will, once during each run from start 

to stop, and consequently \7x:7q = )32-8 times per hour, sustain a 

temporary load of — 

3*3 X 25 = 82'5 per cent, of their rated load. 

The ratio of maximum to average load, taken over the entire 
journey, is often of the order of from 4 to 5 instead of the relatively 
lower ratio of 3*3 obtained in this example. 

For services where such high maxima would be occurring, it has 
been considered desirable to keep the average load down to from 20 
per cent, to 25 per cent, of the rated load. Thus, in a case where 
the average load is 20 per cent, of the rated load, and the maxi- 
mum load is 5 times the average load, then the maximum load 
would work out at 5 X 20 = 100 per cent, of the rated load. In 
most instances of approved modern practice, the maximum load 
to which the motor is normally subjected at frequently recurring 
intervals has rarely been greater than the 1-hour, 75° C. rated load. 
Of course, for occasional grades, such as might occur at points in the 
route, higher loads are sustained, but for the maximum load periodi- 
cally occurring during each run from start to stop, the practical 
experience of years has led to setting this limit. When a motor-coach 
is brought in at the end of a day's constant running at its normal 
schedule, i.e. after from 15 to 18 hours, the thermometric tempera- 
ture rise of the motors should preferably not be more than 65° above 
the temperature of the surrounding air. On the basis of this 
limitation, the maximum temperature at the interior of the windings 
will usually be at least 80° above the surrounding air. If the 
surrounding air should be at a temperature of 25°, this would bring 
the actual temperature of the hottest parts of the motor to at 
least 105°. 

Examples. 

1. Calculate the average tractive force required on a straight and level track to 
accelerate from rest up to a speed of 10 ml ph, in 17 seconds, a train weighing 
200 tons. (Allow 9 per cent, for the momentum of the rotating parts, and take the 
train-friction at 6 kg per ton.) Ans, 7000 kg. 

2. For the conditions in question 1, at the moment when the speed of 10 
ml ph has been reached, what is the power being delivered from the motors to the 
driving axles ? Ans. 307 kw. 

3. What would have to be the percentage down grade in order that the above 
train, after acquiring a speed of 10 ml ph, should continue running at that speed 
without being supplied with power ? (Train-friction, 6 kg per ton.) 

Ans. 0*6 per cent. 



ACCELERATION AND TRACTIVE FORCE 115 

4. Retaining the same tractive effort as in questions 1 and 2, how long would 
it take the train to acquire a speed of 10 ml ph if, instead of starting on a level, it 
started on an up-grade of 1 per cent. ? Ans. 26 seconds. 

5. If, on the other hand, it is desired that it shall still acquire the speed of 10 
ml ph in 10 sec, notwithstanding the 1 per cent, up-grade, (a) what tractive effort 
must be provided, and (h) what will be the power delivered to the axles at the 
instant the speed reaches 10 ml ph ? (Train-friction, 6 kg per ton.) 

Ans. 13,100 kg ; 575 kw. 

6. If the 200-ton train starts on a down grade of 2 per cent., what tractive 
effort must be supplied to provide a constant acceleration of 0*9 ml phps. (Train 
friction, 6 kg per ton.) Ans. 6100 kg. 



CHAPTEE IX 

TBAIN-FBICTION 

It has already been explained that the advantage of electricity over 
steam is most marked for services where the trains stop frequently. 
Since frequently-stopping trains are seldom or never running at 
constant speed for more than a fraction of a minute at a time, the 
energy required to supply the momentum corresponding to the crest 
speed usually constitutes, as we have seen, the greater part, or, at any 
rate, a very large part, of the total energy consumed by the train, and 
the energy required for overcoming train friction is but a small 
proportion of the total energy consumed. Let us now turn our 
attention to the other extreme, where the trains stop only at rare 
intervals, and where, consequently, the energy required to supply the 
momentum is but an insignificant portion of the total energy consumed. 
If we neglect this portion, then there remain but two components. 
One of these components is the energy required for overcoming train- 
friction, i.e. the energy transformed into heat at the bearings, at the 
contacts of the wheels with the rails, and in air friction, and the other 
is the energy supplying the losses in the' electrical equipment, i.e. the 
energy transformed into heat in the electrical equipment. If the 
electrical equipment of the train were of 100 per cent, efi&ciency, then 
the total energy consumed would be exclusively that required for 
train-friction. 

For certain reasons which I shall endeavour to explain in the 
course of this chapter, it is very difficult to analyse the tests which 
have been made to determine train-friction under various circum- 
stances. It appears, however, conclusive that when, over a level and 
well-built permanent way, a train is running at a constant speed, the 
train-friction is very much less than when the train is driven at varying 
speeds, the mean value of which is numerically equal to this constant 
speed. Whereas for speeds fluctuating between and 30 or 40 ml ph 
we have taken 6 kg per ton as a suitable basis for estimating the 
friction component, the appropriate values for constant speeds 
throughout this range, are much less. Several considerations 
influence the values appropriate for different cases, but for a 

ii6 



TRAIN-FRICTION 



117 



representative 100-ton passenger train, the values in Table XXXVII. 
are illustrative of the dependence of the tractive force on the speed. 

TABLE XXXVII. — Teactive Force required for the Propulsion 
AT Constant Speed op a 100-ton Train. 



Speed (ml ph). 


Tractive force required to overcome 


train resistance (kg per ton). 


10 


1-5 


20 


2-5 


30 


3-6 


40 


4.7 


50 


6-6 


60 


8-3 


80 


12-8 


100 


18-5 



The last few speeds in the above table are, of course, much higher 
than can be employed with frequently stopping trains, but they are 
given as of general interest. It is often desirable to add 15 per cent, 
to the values in the above table in order to be conservative. 

Let us take the case of a 100-ton train running at a constant speed 
of 30 ml ph. We see from the above table that the tractive force 
would be of the order of 3*6 X 1*15 = 4*15 kg per ton. Since there 
are 1609 meters in one mile, and since 1 w hr is equal to 367 kg m, 
the energy required at the axles to overcome train- friction is, in this 
case, of the order of — 

4-15x1609 -,01 1. . -1 
^^= = 18 "1 w hr per ton-mile. 

If the train is propelled by motors so geared that, when running at 
their rated speed, the train travels at 30 ml ph, then the conditions 
for this constant- speed equipment will be so very much more favourable 
than in the case of the series -parallel equipments employed for 
frequently stopping trains, that it will be conservative to take the 
over- all efficiency of the electrical equipment as high as 80 per cent. 
The input to the train will then be — 

181 



0-80 



= 22*6 w hr per ton-mile. 



Since the train's speed is 30 ml ph the input may also be expressed 
as (22*6 X 30 = ) 677 w hr per ton per hour, or we may say that the 
jpower required by the train is 677 watts per ton. The total power 
required for the 100-ton train is 67,700 watts. The output from the 
motors is — 

67,700 X 0-80 ^^ . , 
746 = ^2-5 hp. 



ii8 ELECTRIC TRAINS 

Two 40-hp motors would be ample for the work. For such an 
equipment we should not employ the 1-hour rating ; for since the 
train runs at constant speed, the motors would be designed to carry 
their rated load continuously without undue temperature rise. The 
motors would be of the totally enclosed type. The weight of such 
motors is less the greater the rated speed in rpm, but even if they 
are designed for low speed, the weight of the total electrical equip- 
ment would only be of the order of 5 tons. "With forced circulation 
of air the weight of the electrical equipment could be still further 
decreased, but there would not be sufficient justification for this, 
since in any event, the weight of the electrical equipment is only 
some 5 per cent, of the total train weight. 

A 100-ton train for this same schedule speed of 30 ml ph but 
designed and equipped to make one 20-second stop per mile, would 
have an energy consumption of some 160 w hr per ton-mile (see Fig 
45), and would have to carry an electrical equipment (on the 1-hour, 
75° C. basis of rating) of 18 hp per ton, or a total of 1800 hp. If not 
ventilated by forced draught, such a train would probably carry an 
electrical equipment weighing at least 15*5 kg per rated hp. The 
total weight of electrical equipment is thus — 

0-0155x1800 = 28 tons. 

Of the total train weight of 100 tons, some 28 per cent, would 
be represented by the electrical equipment. The weight of the 
electrical equipment of this stopping train is at least some five times 
as great as that of the constant-speed train for the same schedule 
speed. 

This rough comparison has been traced through for the purposes 
of again emphasising the predominating influence of the momentum 
in the operation of city and suburban passenger trains. 

The data which engineers usually have in mind as regards the 
coal burned on a locomotive per train-mile are based on runs of very 
considerable distances between stops, and the natural mistake is liable 
to be made of comparing these coal consumptions per train-mile with 
the coal consumption figures obtained at Electricity Supply Stations 
from which electric trains obtain their power. Obviously, it must be 
remembered that electric trains are usually operated on services 
with frequent stops, and require at the train much greater amounts 
of power than are required by trains hauled by steam locomotives. 
Thus, at 50 ml ph, a non-stopping 100- ton electric train only requires 
some — 

6-6 X 1-15 X 1609 .^ , ^ -T 

367 X 0-80 = 42 w hr per ton-mile. 

This is only half as much energy per ton-mile as is required by a 16 
ml ph 100-ton train making 2 stops per mile. The point to be noted 



TRAIN-FRICTION 119 

is that the particular field for which electric propulsion is so admirably- 
appropriate is in operating city and suburban services, and that if 
steam locomotives could provide the high speeds, together with the 
frequent stops, which are attainable by electrical methods, the coal 
consumption of such steam trains would be much in excess of the 
coal consumption of much faster steam trains making only infrequent 
stops. 

The values given in Table XXXVII. only relate to the train-friction, 
and are exclusive of the friction of the gearing through which the 
power is transmitted from the electric motors to the axles. The motor 
gearing is in most calculations conveniently considered as part of 
the motor, and the gear-friction loss is considered as one component 
of the total loss in the motor. But there is the difference that, 
whereas all the other losses in the motor cease at the instant when 
the electricity is cut off from the train, the gear loss continues so long 
as the train is in motion. Thus, the deceleration during coasting (i.e. 
drifting) is proportional to the train-friction plus the gearing friction. 
The gearing friction is by no means negligible in comparison with 
the train-friction. On the contrary, it constitutes a very important 
component of what we may, for convenience, term the " inclusive " or 
" over-all," friction. 

The question is so important as to justify us in working out a 
case. Let us consider a motor-coach with an electrical equipment 
comprising two 150-hp motors. The complete weight of the motor- 
coach, including the electrical equipment, is 39 tons. At a speed of 
45 ml ph the frictional resistance, exclusive of gearing, may be 
taken at 5*4 kg per ton, this value corresponding roughly with the 
data in Table XXXVII. If the load consisted exclusively of the 
train friction, then at 45 ml ph the output from the two motors 
would be calculated as follows : — 

Total tractive force = 39 x 5*4 = 210 kg 

^ , 45 X 1609 „^ . 
Speed = — ^^ — = 201 m ps 

Output = 210 X 201 = 4230 kg m ps 
= 4230 X 9-81 = 41,400 watts 

_ 41,400 _ 

- 746 - 00 o np 

This is, of course, a very small load for an equipment with 300 
aggregate rated hp ; the output per motor is only — 

^ = 27-6 hp, 
or 18 4 per cent, of the rated load of the motor. 



120 ELECTRIC TRAINS 

At rated load of 150 hp the gear loss in this motor is 4 per cent, 
of the output, thus being — 

150 X 746 X 0*04 = 4480 watts. 

The gearing loss in railway motors may, for rough calculations, be 

taken constant at all loads. At 45 ml ph the friction loss of the 

train, inclusive of gearing, is 41,400 + 2 x 4480 = 50,360 watts, 

and this is the load delivered from the armature axles of the 

motors to their gearing. The train-friction, inclusive of gearing, 

is thus — 

50,360 ^ . ^ ^ , , 

2j^ X 5-4 = 6-6 kg per ton, 

of which (6'6 — 5*4 =)1'2 kg per ton is due to the gearing. Had 
the motor-coach been provided with four motors instead of with two 
motors (and this is very often the case), then the friction of the motor- 
coach would have been (5*4 + 2 X 1'2 =)7'8 kg per ton. In this 

(T.O ^ 

case we should have a (y^ = 1'45 j45 per cent, higher frictional 

resistance per ton than would be obtained with a trailer-coach. In 
this case, when all the four axles carry motors, the increased electrical 
equipment will bring the weight of the motor-coach up to 46 tons. 
Let us, from this point onwards, keep such a four-motor equipment in 
mind. The equipment is amply able to operate a heavy train of 
trailers at the speed in question, namely, 45 ml ph. Let us add five 
trailers, each of a weight of 26 tons. Thus, the five trailers will, at 
45 ml ph have a resistance of (5 x 26 X 5*4 = )700 kg as against 
the resistance of (46 X 7'8 =)360 kg for the four-motored coach 
which hauls the train. The total weiofht of the train is — 

46 -I- (5 X 26) = 176 tons, 
and the average train- friction is — 

700 -j- 360 1060 ^ ^ , 

YfQ = jrfQ = o-O kg per ton. 

The longer we make the train by the addition of trailers, the 
more nearly will the train-friction approach 5*4 kg per ton. In 
Table XXXVIII. are worked out the values for trains with one 
motor-coach, and successively 1, 2, 3, 4 and 5 trailers. 



TRAIN-FRICTION 



121 



Table XXXVIII. — Showing the Influence on the Total Frictional Eesist- 

ANCE OF A TeAIN, OF ADDING TbAILER-COACHES. 











<^ i. 




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. 


V /~s 




V V 

IP 


a 


IS 
|§ . 

©as 

o o 


§ o "»> . 

list 


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® R o 




.2 2 


2 a 
g o 

oS ♦^ 

.2S 

on a, 

— 1 J«l 


ftl - 


3 2 "^ 


^^ 


■^ <j a 


5 <- -s y 




a m a ^ 


C o 


08 ^^ 


MB 

a 








a o G -^ 


s. o 




§.2 

is 


1 


IM 


46 


\ 


/ 






360 


7-8 


2 


IM + IT 


72 








26 


140 


500 


7-0 


3 


1M + 2T 


98 




46 


360 ■ 


52 


280 


640 


6-5 


4 


IM + 3T 


124 




78 


420 


780 


6-3 


5 


IM + 4T 


150 








104 


562 


922 


6-1 


6 


IM + 5T 


176 


/ 




\ 


130 


700 


1060 


6-0 



In the above example I have laid stress on one of the two 
important influences in virtue of which long trains (usually also 
heavy trains) demand a lower tractive force per ton of weight than 
short (usually also light) trains. 

A second influence the importance of which is very dependent 
upon the speed, relates to air friction. Air friction only commences 
to be of importance at speeds of some 30 ml ph, and the air resist- 
ance in kg per ton is less the greater the length of the train. The 
train-friction values in Table XXXVII. were given for 100-ton 
trains, so that they will be applicable to the 3-coach train of Table 
XXXVIII. Now, with a shorter train, the frictional resistance per 
ton, other than air friction, will increase in the manner which has 
just been determined, but the air resistance per ton will also be 
greater, due to the predominating influence of the air friction at the 
front and rear of the train, and will tend to accentuate the differences. 
Considering, then, the resistance of the 3-coach train as correct, the 
values for the other trains, when this change of air resistance is duly 
considered, wdll conform more to the dotted curve in Fig. 63, where 
the full-line curve is that plotted from the results in Table 
XXXVIII. The frictional resistance of the 3-coach train is taken 
the same in both cases. 

A series of tests were made at Zossen,* near Berlin, in 1903, to 
determine the frictional resistance of electric trains at high speeds. 
Some of the results are given in Table XXXIX. (p. 122), where the 
component resistances are shown. It is seen from the table that at 
about 40 ml ph the air resistance, for the conditions of the Zossen 



*' A detailed description of the Berlin-Zossen Tests is given in " Electric Kailway 
Engineering," by Parshall and Hobart (Constable and Co., 1907). 



122 



ELECTRIC TRAINS 



tests equalled the remainder of the frictional resistance. In the 
values of the frictional resistance given in Table XXXVII. the air 
resistance has been included as part of the total train resistance. 



ll 


8 


Js 




^ 




-^ 


6 


•5 




\> 




to 




J; 




"§ 


4 


% 




^ 




^ 




% 


Z 


^ 







\ 
\ 




















\ 


\ 




















\ 




k^ 


















^v 


"^"^^ 


•^^ 


. 




















■*^-* 


























































































Co» 


:hcs 


/ 


z 


3 
1 




4- 
J 




e 

L 





-^ Qo m 

7rfi/n )1^/^hd 



/60 



eoo 



Fig. 63. — Curves showing Tendency of Train Eesistance to decrease with 
Increased Weight of Train. 

Table XXXIX. — Values of Frictional Resistance deduced prom the Berlin- 
ZossEN Tests with an 83-ton, 75-poot Coach. 



Speed in ml ph. 


Mechanical resistance 

(track and axle friction) 

(kg per ton). 


Air resistance (kg per ton) 


Total frictional resistance 
(kg per ton). 


40 


2-2 


2-3 


4-5 


50 


2-4 


3-6 


6-0 


60 


2-6 


6-3 


7-9 


70 


2-8 


7-0 


9-8 


80 


30 


9-0 


120 


90 


3-2 


11-4 


14-6 


100 


3-4 


14-2 


17-6 


110 


3-6 


17-8 


21-4 



A third factor, which does not in reality affect the train resistance, 
but which at first sight obscures the matter, is the varying efficiency 



TRAIN-FRICTION 123 

of the electrical equipment with varying load. Time and again, tests 
have been published in various countries, the results of which 
appeared to indicate a very remarkable diminution in the train 
resistance per ton, for long trains, as compared with short trains. I 
am of opinion that much too great a portion of the decreased input 
to the train (per ton of its weight) with increased weight of train, has 
been ascribed to decreased air friction, and that a factor of great 
importance has been overlooked. This factor relates to the increas- 
ing efficiency of the electrical equipment with increasing load, i.e. 
with increasing number of trailers hauled. The curve in Fig. 60, on 
p. 105, shows conclusively that there is a very considerable increase 
in efficiency with increasing load, even for a comparatively small 
range in the values of the loads carried by the motors. The results 
in Fig. 60, however, refer to runs with frequent stops, and are there- 
fore not directly applicable to the present case of constant-speed 
running. The variation in the efficiency of the electrical equipment 
is even more pronounced when a test is first run with a single motor- 
coach at such a speed, or under such conditions, that the equipment is 
only very lightly loaded, corresponding tests afterwards being made 
with the motor-coach hauling enough trailers to load the motors well 
up toward their rated capacity. 

Let us take our 46-ton motor-coach, with its equipment of four 
150-hp motors, and let us roughly estimate the input for a speed of 

45 ml ph, first when the motor-coach is running without any trailers, 
and: afterwards with 2, 4, 6 and 8 trailers. The motor-coach weighs 

46 tons, and each trailer-coach weighs 26 tons. Consequently, our 
calculations will relate to 5 trains weighing respectively 46, 98, 150, 
202 and 254 tons.; Let us ignore the variations in the air resistance 
per ton with increased length of train, in order to be the better able 
to study the influence to which we wish at this point to chiefly direct 
our attention. The calculations in this case are facilitated by con- 
sidering the gearing to be part of the motor. We shall consequently 
take the train-friction throughout at 5 '4 kg per ton. The tractive 
forces in the five cases are thus, 248, 529, 810, 1090 and 1370 kg, as 
set forth in Table XL. From the tractive force we determine the hp 
output of the motors when operating the trains at 45 ml ph {i.e, 20*1 
m ps) in the same way already employed earlier in this chapter. There 
being four motors, the output per motor is 25 per cent, of the total 
output ; and then by referring to the efficiency curve of a typical motor 
of the same rated hp (Fig. 43 on p. 72) the respective efficiencies of the 
motor at these outputs are obtained. It is seen that the first train, 
consisting of a motor-coach and no trailers, only requires 11 per cent, 
of the rated output of the motors when running at this constant 
speed, and the efficiency of the motors consequently has the low value 
of 40 per cent. During these tests the motor efficiency is the only 



124 



ELECTRIC TRAINS 



factor that need be considered, in order to arrive at the results in 
view. When two trailers are added, it is seen that the motor efficiency 
rises to 75 per cent., and that the load is 23 per cent, of the rated 
output. This case (the 98-ton, 3-coach train) is taken as the repre- 
sentative one for operation by one motor-coach, and the other trains 
are referred to it. In tests similar to those under consideration in 
this chapter, it would appear that the tractive force has frequently 
been erroneously deduced from the readings of the electrical input to 
the motors, and serious error would appear to have been involved, 
owing to taking a constant efficiency for the electrical equipment, i.e. 
it would appear that the output has been taken as being a constant 
ratio to the input, or that insufficient allowance has been made for 
the change in efficiency with load. For instance, in the case of the 
5-coach train, the true motor efficiency is some 83 per cent., but if the 
75 per cent, efficiency were adhered to (as in the standard 3-coach 
train) the true tractive force would be greater than the apparent 
tractive force (obtained by employing this 75 per cent, efficiency) in 
the ratio of — 



(810) to (^810 X 



76\ 
'83/ 



that is, in the ratio of 810 to 730. In other words, the equipment 
would have been credited with 8 per cent, less efficiency than it was 
really yielding, and hence the frictional resistance was in reality 
greater than was ascribed to it. 

Table XL.— Showing the Influence op the Inceeased Efficiency op Elec- 
trical Equipment (with incbeased load) on the Frictional Resistance, 
AS deduced from Readings of Electrical Instruments during tests with 
AN Assumed Constant Efficiency for all the Tests. , 



Number of coaches 
in train. 


Make-up of train : 
M = motor-coach. 
T = trailer-coach. 


m 

P 

.a 

u 
o 

to 

'S 


Frictional resistance 

(kg per ton) (gear loss 

included in motor 

losses). 


"no 

<u 

i- 
—1 ^^ 

a to 

§cS 

'43 a 
u o 
u P 

fa »s 

§ 


^ ftp* 

*=-p fl 

•3 V-/P 

■3§o 

&=2a 

65-5 
140 

214 
288 
362 


t-l 

S 

o 

a 

p< 



"3 
o 


Percentage which this 
output is of the rated 
load of motor (150 hp). 


Efficiency of motor at 

this output, including 

gear loss (Fig. 43). 


Apparent frictional re- 
sistance which would 
be obtained from elec- 
trical readings, assum- 
ing 15 per cent, 
efficiency throughout. 


Corresponding appa- 
rent frictional resist- 
ance (kg per ton). 


True frictional resist- 
ance, including gear 
friction (kg per ton). 


1 

3 
5 

7 
9 


IM 
IM -f 2T 
1M+4T 
lM-f6T 
IM + 8T 


46 

98 

150 

202 

254 


' 5-4 , 

/ 


V 


248 

529 

810 

1090 

1370 


16-4 
35-0 
53-5 
72-0 
90-5 


11 

23 
36 
48 
60 


40 

75 
83 
87 
88 


465 
529 
730 
940 
1170 


10-1 
5-4 
4-9 
4-7 
4-6 


7-8 
6-5 
6-1 
5-8 
6-6 



A total tractive force of 730 kg corresponds to an apparent 
frictional resistance of 4*9 kg per ton, as against the true value 
(exclusive of gear loss) of 5*4 kg per ton. The error is particularly 



TRAIN-FRICTION 



125 



striking in the first case in the table, where the train consisted of a 
single motor-coach, and where the efficiency, owing to the light load, 
is very low, and where, consequently, the apparent value for the 
tractive force is much greater than the true value. 

The last column shows that the effect of overlooking the change 
in motor efficiency would be to give an erroneous impression that the 
anticipated result had been obtained — that is, that there had been a 
great diminution in the frictional resistance with increased train 
length. The apparent results accentuate beyond its true value, the 



iZ 



10 



^ 

^ 

tl 

i 

^ 











\ 




























\ 


s. 




























\ 






























\ 


*». 




























\. 


V. 






























"^ 




— 


















































































































































Jfum 


^roj 


Coai 


hes 


Z 
.1, 


3 

1 






S 


€ 
,--1, 




f 







40 



do 



/eo /60 

Train height- 



aoo 

Tons. 



240 



Fig. 64. — Curve showing Change of Tractive Eesistance with Weight of Train as 
obtained from Kesults of Tests given in Table XLI. 

diminution with increasing length of train, of the frictional resist- 
ance per ton weight of train. 

Some interesting tests have been made by Armstrong, Potter, 
Aspinall and oth-ers to investigate the change of tractive resistance 
with increased train length, and the results fully confirm the general 
considerations which have been set forth in this chapter. 

Aspinall has published results of some very complete tests* carried 
out with a view to obtain the effect of varying length of train. Table 
XLI. gives the average values obtained, and these are plotted in Fig. 64. 



"Proceedings of the Institution of Civil Engineers," vol. clxxix. p. 121. 



126 



ELECTRIC TRAINS 



Here it will be seen that the tractive force decreases from 107 
kg per ton when the train consists of two motor-coaches and no 
trailers, down to 6 '5 kg per ton when five trailers are added. If the 
trailers are only debited with a tractive force equal to the increase 
of the total input to the train over the input required by the motor- 
coaches alone the tests would appear to indicate that the tractive force 
per ton of added trailer would be of the values entered in the last 
column, i.e. some 3'5 kg per ton of trailer, as against some 10'7 kg per 
ton of motor-coach. 



Table XLI. — Aveeage Values 


OF THE ; 


Results obtained 


DUEiNG Tests 


OP the 




Teactive Resistance on Lancashiee ane 


YoEKSHiEE Railway. 




to 

1 


Make-up of train : 
M r= motor-coach. 
T = trailer-coach. 




d 
'3 




effort 
:ome 
iction, 
from 


5- c d 
-2 .2 -3 


&0 <c 




to 00 


8.S 

r 


Length of 
train. 


, O CD 

-u d 


Speed of tr 
observed 2J m 
after start (m 


Total tractive 

(kg) to over< 

"over-all" fr 

as calculated 

readings 


Tractive effo 
" over-all " fn 
kg per ton of 


Trailer wei 
added (ton 


Extra tract 

effort (kg) to 

come frictio 

trailers. 


Tractive fore 

per ton, f 

friction of tra 






(ft) 


Cm) 
















2 


2M only 


124 


38 


92 


51-7 


984 


10-7 


— 


— 


— 


3 


2M + 1T 


186 


57 


118 


49-9 


1071 


9-1 


26 


87 


3-4 


4 


2M-F2T 


248 


76 


144 


47-6 


1148 


8-0 


52 


164 


3-2 


6 


2M4-3T 


310 


95 


170 


45-7 


1230 


7-3 


78 


246 


3-2 


6 


2M + 4T 


372 


114 


196 


42-5 


1320 


6-7 


104 


336 


3-8 


7 


2M-1-6T 


434 


133 


222 


40-3 


1458 


6-5 


130 


474 


3-6 



While the published results are not accompanied by data permit- 
ting of confirming my opinion, it nevertheless appears to me that, 
notwithstanding that each motor-coach had four motors and, conse- 
quently, four sets of gearing, it is probable that, at the speeds indicated 
in the table, the tractive force, including the friction of the gearing, 
would, per ton of motor-coach, have been more of the order of 8 kg, and 
that the further 33 per cent, of apparent tractive force in the case of the 
2-coach train is to be accounted for by the very high percentage of loss 
in the electrical equipment, since the motors, when no trailers were 
included in the train, were only loaded up to some 18 per cent, of 
their rated capacity, and would, consequently, have only very low 
efficiency. Conversely, a trailer friction of some 5 kg per ton in 
place of the 3*5 kg per ton could be arrived at by crediting the 
electrical equipment with a much higher efficiency, owing to the 
much greater percentage of rated load at which it was working. For 
it must be kept prominently in mind that a higher efficiency of the 
electrical equipment means a lower percentage of losses in the 
electrical equipment, and hence, for a given input, higher losses 
due to train resistance. These suggestions are only put forward 
as a view which, whether justified or not justified in the case of 



TRAIN-FRICTION 



127 



these particular tests, should be carefully considered, as it has an 
important bearing on the subject of train-friction. 

The higher tractive resistance of motor-coaches which we have 
considered, at once throws light on similar efifects observed with electric 
locomotives in which geared motors are employed. Hutchinson * has 
carried out tests of the frictional resistance of some steam and electric 
locomotives. 

The tests were first suggested by the energy required to haul trains 
through tunnels, when an idle steam locomotive constituted part 
of the trailing load. Hutchinson says, " The power required to haul 
these trains seemed greater than it should be ; investigation showed 
that the difference was accounted for by the unexpectedly high 
frictional resistance of the steam locomotives as a trailing load." 
Tests were made (at a speed not stated in the paper) by towing the 
steam locomotives behind an electric locomotive fitted with test 
instruments, and the total tractive effort was deduced from these tests. 

Table XLII. — Values op the Frictional Besistancb op Locomotives as 
determined from tests by hutchinbon. 



Locomotive claBsification. 


Total weight of 

locomotive 

with tender. 


Net frictional 

resistance 

of locomotive 

and tender (kg). 


Frictional 

Eesistance 

(kg per ton). 


MaUet No. 1904 .... 
Mallet No. 1911 .... 
Mallet No. 1905 .... 
Consolidation. .... 
Pacific ...... 


250 
250 
250 
150 

188 


4910 
4090 
7120 
2480 
1760 


19-5 
16-3 
28-6 
15-7 
9-4 


Electric 


115 


680 


5-9 



Previous tests on trailing coaches gave a figure of 27 kg per ton 
for the tractive resistance. This allowance was made for the electric 
locomotive in the above tests, and after making corrections for the 
grade, the frictional resistance was obtained. The results are given 
in Table XLII. for five steam locomotives and one electric loco- 
motive. The frictional resistance of a steam locomotive and tender 
is seen to average 18 kg per ton — in one case reaching the high 
value of 28*6 kg per ton. The total resistance of the electric loco- 
motive, including the friction of the gearing and motor bearings, was 
5*9 kg per ton — a value over twice as great as that obtained for 
the trailing rolling stock. 

Another set of test results of great interest, and bearing on the 



* " Transactions of the American Institute of Electrical Engineers," vol. xxviii 
p. 1436. 



128 



ELECTRIC TRAINS 



subject of this chapter, are those obtained by Davis and analysed 
by Armstrong.* In Table XLIII. are given the results at which 
Armstrong arrived for the train-friction at various speeds for three 
cases— first a 280-ton train, then a train of 70 tons, and finally a 
35-ton single coach. The tests indicated that trains heavier than 
280 tons did not have an appreciably lower tractive resistance. 

Table XLIII. — Values of the Tractive Resistance op Trains op Various 
Weights, as obtained prom Armstrong's Analysis op Tests by Davis. 



Speed (ml ph). 


Tractive resistance (kg per ton). 










280-ton train. 


70-ton train. 


35-ton 
single coach. 


20 


4-1 


5-0 


5-7 


30 


50 


6-8 


8-6 


40 


5-9 


9-4 


12-5 


50 


7-0 


12-2 


17-2 


60 


8-2 


15-4 


22-4 


70 


9-4 


19-2 


28-2 


80 


10-7 


23-7 


34-0 



This chapter has so far been devoted to considerations of the 
tractive effort at constant speed; but there are similar effects of 
increased train weight on the energy consumption, when we come to 
services with frequent stops, such, for instance, as would occur in 
city and suburban services. As an instance of tests to determine the 
energy consumption for frequently-stopping trains of various weights, 
Table XLIV. is given. The table relates to tests made by Arnold and 
Potter.t 

Table XLIV. — Arnold and Potter's Results op Tests for the Energy 
Consumption of Trains of Various Weights under Service Conditions 
(One Mile Run). 



Make-up of train : 
M = motor-coach. 
T ^ trailer-coach. 


Weight of train 
(tons). 


"Weight of 

trailer-load 

(tons). 


Maximum 

speed during 

the ruu 

(ml ph). 


Average speed 

during the run 

(ml ph). 


Energy con- 
sumption (from 

watt-meter) 
(w hr per ton- 
mile). 


2M only 
2M-MT 
2M -i- 2T 
2M4-3T 
2M-f4T 
2M + 5T 
2M + 6T 


64-5 
85-0 
106-5 
133-5 
158-0 
181-0 
206-0 


20-5 
42-0 
69-0 
93-5 
116-5 
141-5 


46-7 
44-7 
42-8 
41-0 
39-1 
37-9 
36-4 


34-6 
33-1 
32-0 
30-6 
29-8 
28-6 
27-2 


143-0 

127-0 

111-0 

104-0 

96-5 

91-1 

88-3 



* " Transactions of the American Institute of Electrical Engineers," vol. xxii. p. 91. 
t Ibid. vol. xix. p. 836. 



TRAIN-FRICTION 



129 



The trains consisted first of two motor-coaches, and then successive 
additions of 1, 2, 3, 4, 5 and 6 trailer- coaches, each motor-coach weigh- 
ing about 32 tons against an average trailer-coach weight of 23 tons. 

Some interesting curves of train friction for varying weights of 
train have been plotted in Fig. 65. They are based on Aspinall's 
formula,* in accordance with which the train friction per ton of 

weight of train is equal to a + 1 — ; — t, where a, h and c are constants, 

6 -f cL 

Z4 












k^ 



20 

IB 

It 
10 
8 
6 
4 
2 























A, 


tet 
























J 
























/ 


/ 
























^ 


/y 


/° 






A =507on7r7»m 
a ■'/OO • 
C ^200' • 
D ^400 ' - 
£=300' ' 








// 


V, 


/ 


^c 










A 


V. 


/ 


/ 


A 









/, 


V. 


'/ 


y 


/ 






A 


^ 


y 


y 


/ 
















/^ 


0. 


^ 


y 


















> 


^ 


y 


y 


















^ 


^ 


^ 












































/ 


Z 


V ^ 


4i 


^ 


6 


^ 


7 & 


5 


V K 


70 •/< 


/i 


V 



Fig. 65. — Curves showing the Tractive Resistance for Trains of Various Weights. 

V is the speed of the train in ml ph, and L the length of the train in 
feet. By assuming a representative weight per foot of over-all 
length of train, the curves of Fig. 65 have been deduced for trains 
of a total weight of 50, 100, 200, 400 and 800 tons.f 

Influence of Curves on Frictional Resistance 

Curvature of the track adds very considerably to the tractive 
effort necessary for train propulsion, and the additional effort 

* " Proceedings, Institution of Civil Engineers," vol. cxlvii. p. 241. 

t The variation of the train friction, and also the variation of the energy con- 
sumption, with trains of different weights, have been investigated very fully at pp. 14- 
16 of *' Electric Kailway Engineering" (Parshall and Hobart). 

K 



130 



ELECTRIC TRAINS 



required depends largely upon the degree of curvature, and also on the 
rigidity and gauge of the track, and on the wheel base of the coach. 

The method by which track-curvature can be evaluated involves 
the angle which a given length subtends at the centre of the curva- 
ture. One way of expressing this curvature is by the degrees sub- 
tended by a chord 100 feet in length. The extra tractive effort 
required is taken as proportional to this figure. From numerous 
experiments to determine the train-friction on curves, an average of 
0*32 kg per ton per degree has been found to agree closely with the 
various experimental results. This is the additional effort required 
on the track, quite apart from friction at the axles, ordinary friction 
between rail and wheel, and air friction. The most important 
formulae which have been put forward are those of Blondel-Dubois 
and Dupuy. The former gives the additional tractive effort as — 

574 

-^ kg per ton 

where E = Eadius of curve in meters. The latter authority gives — 

370 , 
E^TTO ^^ P"^ ^^^- 
Both these formulae apply to the standard gauge of track. 

Values for the additional tractive effort required on curves have 
been worked out by these three methods, and the results are set 
forth in Table XLV. It will be seen that they are in close agree- 
ment over the whole range of radii. The tractive resistance on any 
curve can then be computed from the values for straight track by 
adding the amount corresponding to the curve under consideration, 
as obtained from Table XLV. — 

Tabl!b XLV. — Additional Tractive Effort required on Curves. 





Radius of curve. 




Additional tractive effort required (kg per ton). 








Estimated from 
the value of 


Estimated from 


Estimated from 


Meters. 


Feet. 


Chains. 


the formula of 


the formula 








0*32 kg per ton 
per degree. 


Blondel-Dubois. 


of Dupuy. 


30 


99 


1-5 


19-10 


19-20 


18-50 


40 


132 


2-0 


14-10 


14-30 


12-30 


50 


165 


2-5 


10-90 


11-50 


9-26 


60 


198 


3-0 


9-10 


9-57 


7-40 


80 


264 


4-0 


7-05 


7-19 


5-29 


100 


330 


5-0 


5-45 


5-75 


4-11 


120 


396 


6-0 


4-55 


4 79 


3-36 


160 


528 


8-0 


3-45 


3-59 


2-46 


200 


660 


10-0 


2-77 


2-87 


1-95 


300 


990 


15-0 


1-81 


1-92 


1-27 


400 


1320 


20-0 


1-41 


1-43 


0-96 


600 


1980 


30-0 


0-91 


0-96 


0-63 


1000 


3300 


50-0 


0-55 


0-58 


0-37 



TRAIN-FRICTION 131 

Examples. 

1. A 135-ton train maintains a schedule speed of 22 ml pb, making a 20-second 
stop every 0"9 ml. It consists of two motor-coaches and one trailer. Each motor- 
coach weighs 50 tons, and the trailer weighs 35 tons. Each of the four axles of each 
motor-coach carries a geared motor. On a straight and level, well-built track what 
would be your estimate of the average frictional resistance of this train when operating 
to the above schedule ? 

2. Allowing 12 per cent, for rotational momentum, and taking the over-all effi- 
ciency of the electrical equipment as 70 per cent, when operating to the above 
schedule, work out the energy consumption in w hr per ton-mile. 

3. If, in the above case, 40 per cent, of the distance consists of curves of 150 
meters radius, the remaining 60 per cent, being straight, estimate the energy con- 
sumption on the basis of the same over-all efficiency of the electrical equipment, 

4. If, of the 135 tons total weight of train 40 tons represents the aggregate weight 
of the single-phase electrical equipment (which has a rated capacity of 920 hp), 
then, if 920-hp of continuous equipment weighing only 19 kg per hp, and comprising 
only 4 motors (instead of 8), were substituted, calculate the reduction in the input to 
the train, taking the rotational momentum at only 8 per cent, of the translational 
momentum, and again taking the over-all efficiency of the electrical equipment at 
70 per cent. 

5. The train, equipped with continuous apparatus as indicated in question 4, 
would weigh 117 tons, and only 4 axles (instead of 8) would carry gears. Taking 
into account the reduced input, there would no longer be occasion to instal as much 
as 920-hp aggregate rated capacity of motors and equipment. To what rated 
capacity should this be reduced in order that the average load on each motor, taken 
over the entire run, should constitute the same percentage of the rated load, as in 
the case of question 2 ? Make a new estimate of the total train weight to accord 
with this new estimate for the aggregate capacity of the electrical equipment, which 
may be again taken at 19 kg per rated hp. 



CHAPTER X 

THE FBEDETERMINATION OF THE POWER CURVE FOR A 

GIVEN JOURNEY 

The principles enunciated in the preceding chapters afford guidance 
in selecting suitable electrical equipment as regards rated hp and 
other general features. But as the work on a proposition advances 
there arrives a stage at which it becomes important to investigate, 
with considerable care, the application of some particular motor and 
equipment to the particular case in hand. 

Let us take a case where it is required to operate 150-ton trains, 
consisting of two motor-coaches and four intermediate trailers, to a 
schedule speed of 25 ml ph, with 1 stop per mile. From Fig. 45 we 
find that the energy consumption will be 97 w hr per ton-mile. This 
works out at — 

97 X 25 = 2420 watts per ton. 

The average input to the train will be — 

2-42 X 150 = 363 kw. 

From Table XXV. we obtain 70 per cent, as a rough value for 
the over-all efficiency of the electrical equipment. The average out- 
put from the motors is thus — 

363 X 0-70 ^ ._ , 
0-746 = ^^^ ^P- 

Let the service for which we shall employ these trains be absolutely 
continuous for 18 hours per day — or, at any rate, let it be required 
that the train and equipment shall be adequately designed for such a 
performance. It will then be necessary that the electrical equip- 
ment shall have a rated capacity (on the 1-hour, 75"^ C. basis) of — 

4 X 340 = 1360 hp, 

since the average output for such a service is about 25 per cent, of 
the rated output (see p. 75). 

132 



POWER CURVES 133 

Let this aggregate capacity be made up of 8 motors, 4 on each 
motor-coach. The rated capacity of each motor will thus be — 

1360 ,^^^ 
-g- = 170 hp. 

For a schedule speed of 25 ml ph, with one 20 -second stop 
per mile, we see, from Fig. 44, that the maximum speed must be 
41-0 ml ph, or — 

41-0x1609 ,,^^ 

- =1100 meters per mmute. 



60 

Let the car wheels be of 1000 mm diameter. The speed of the 
car wheel is, at the maximum train speed of 41 ml ph — 

1100 ..^ 

^r-— r = doO rpm. 

1-00 X TT ^ 

The question of the relative speed of motor armature and car axle 
is one of considerable importance. In general, the lower the speed 
of the motor, the better will be its performance, but, on the other 
hand, the lower its speed the greater is its weight. With the advent 
of interpoles it has become legitimate to employ higher motor 
speeds, nevertheless, the weights of equipments employing series- 
wound, continuous-electricity motors are not great, and it is expedient 
to retain fairly low motor speeds. The higher the train speed, the 
lower, consequently, should be the gear ratio. For locomotives 
required for crest speeds of 65 ml ph, or more, a 1 : 1 ratio is usually 
employed. On the other hand, for motor-coaches for speeds of 14 to 
18 and 20 ml ph, with a stop every 0*5 to 0*8 of a mile, the gear ratio 
is usually taken in the neighbourhood of 3'0 to 3*5 in continuous 
equipments, while in single-phase equipments for such services, gear 
ratios as high as from 4 to 5 are taken, since otherwise the motors 
would be very heavy. As instances of the precise number^ of teeth 
on gears and pinions which are suitable in practice, Table XLVI. is 
of interest. 

Let us for our case take a gear ratio of 2 '47, providing the 
motor with a pinion with 21 teeth and the car axle with a gear 
with 

2-47 X 21 = 52 teeth. 

Since the gear ratio is equal to 2*47, the speed of the armature when 
the train is running at its crest speed is — 

350 X 2-47 = 865 rpm. 

Let us proportion the equipment to provide a speed of 20 ml ph at 



134 



ELECTRIC TRAINS 



the end of 15 seconds from the start, maintaining during these first 
15 seconds an acceleration of — 

rrv = 1*33 ml phps. 
lo ^ ^ 

Let the last section of the rheostat be cut out at the end of the 15th 
second, i.e. when the train has acquired a speed of 20 ml ph, and 
let the balance of the acceleration up to 410 ml ph be accomplished 
on the "motor characteristic." If the crest speed of 41*0 ml ph 
is to be reached at the end of the 80th second, as shown in the 
diagram in Fig. 66 (which is substantially identical, although drawn 
to a different scale, with the diagram in Fig. 44), then the design of 
the motor, as regards its saturation curve, must be such as shall, with a 
150-ton train equipped with eight such motors, provide the acceleration 
indicated in Fig. 66 for the time from the 15 th to the 80 th second. 



Table XLVI. — Data of Gear Eatios of Several Typical Motors. 



o a, 

to 2 

C i 


Railway. 


Type of motor. 


Hated 

bp of 

motors. 


Speed of motor 

at its rated 

(1-hr, 15° C.) load. 


60 

a 

!P 

i-iS 

S « 
% « 

it 

ft 


Gear 
ratio. 


Number of 
teeth. 


)f train at 
load of 

)tor8. 




Pinion. 


Gear. 


CO 










(rpm). 










(mlph) 


1 


Lancashire 1 
and Yorkshire j 


Dick-Kerr 


150 


470 


1067 


1-95 


22 


43 


30 


^ 


Central ) 
London Bailway ) 


G.E. 66A 


125 


660 


889 


3-94 


ri5 

(18 


591 
71/ 


17-5 


o 

^ ( 


Great Northern^ 
Piccadilly & Br. j 


G.E. 69B 


200-240 


530 


914 


3-20 


— 


— 


17-8 


^ J 
o 1 

O 1 


Lancashire "1 
and Yorkshire j 


D.K. 5A 


125 


625 


914 


2-16 


19 


41 


31 




Liverpool | 
Overhead / 

t 


D.K. lOOA 


100 


570 


838 


2-79 


19 


53 


20 


\ 


D.K. 12HT 


150 


640 


1067 


3-33 


15 


50 


24 


/ 


Midland 


Westinghouse 


150 


625 


1105 


3-68 


19 


70 


22 




Midland 


Siemen's 


180 


770 


1105 


2-93 


30 


88 


34 


tc 1 
e3 1 

<D \ 

-HI) 


L.B. &S.C. f 
Railway 


A.E.G. \ 
W.E. 51 / 


115 


600 


1105 


4-26 


— 


— 


18-2 


Hamburg- ( 
Blankenese \ 


A.E.G. \ 
W.E. 61 / 


115 


600 


1000 


4-22 


— 


— 


16-7 


.2 1 


( 


G.E.A.603 1 
















m 1 


- 1 


Compensated 
series 


100 


650 


1067 


3-74 


19 


71 


22 



We have seen in Chapter VIII. that the tractive force required to 
impart an acceleration of 1*0 ml phps is 49*5 kg per ton. Consequently, 



POWER CURVES 



135 



our 150-ton train will, during the first 15 seconds, require a tractive 
force of — 

1-33 X 49-5 = 65-9 kg per ton 

for acceleration, and a further 6*0 kg per ton to overcome train-friction. 
Thus, the total tractive force will be — 

65-9 H- 6-0 = 71-9 kg per ton. 



50 



40 






30 



5^ 



^^ 



/o 









































































































""^ 


\ 














,/ 


X' 












\ 












/ 
















\ 










/ 




















\ 








/ 




















\ 






1 


r 




















\ 




























\ 


I 




1 
























\ 






z 





4l 





<^ 


') 


d 


d 


/c 


x> 


/^ 


b 


/4 



7//ne /n ^econcfs 

Fig. 66. — Speed-time Diagram for Emi of one mile at a Schedule Speed of 

25 ml ph. 

The tractive force to be provided by each of the 8 motors is — 

71-9 X 150 



At 20 ml ph, i.e. ( 
will be — 



8 

20 X 1609 
3600 



= 1350 kg. 



= j8"9 m ps, the output per motor 



or 



1350 X 8-9 X 9-81 = 118,000 watts 
118,000 



746 



= 158 hp. 



At this point, when the speed is 20 ml ph, the last resistance section 
has been cut out and the motor is directly across the 600 -volt line. 
The efficiency of a series-wound, continuous-electricity motor of this 
rating is, including gearing, usually between 85 and 88 per cent, at 



136 ELECTRIC TRAINS 

all loads between half-rated load and 50 per cent, overload. But 
taken over the period while electricity is on, the efficiency will be 
more of the order of 80 per cent. Taking the efficiency as 80 per 
cent, the input is — 

118,000 ..oAHA ^. 

^ Q^ = 148,000 watts, 

and the current to the motor is — 

148,000 



600 



= 246 amperes. 



This is approximately the value of the current for the first 15 seconds, 

although it will have fluctuated by equal amounts, above and below 

this value, in passing from notch to notch, i.e. in the process of 

cutting out, step by step, the resistance in series with the motor. 

We see from Fig. 66 that in the interval from the 15th to the 20th 

second it is desired that the speed shall increase from 20 to 24*5 ml ph, 

/4*5 \ 
the mean acceleration thus being ( ^ = )0'90 ml phps. 

The average tractive force per ton will consequently be only — 

0-90 X 49-5 + 6-0 = 44-5 + 6-0 = 50*5 kg. 
The average speed during this 5 -second interval will be — 

20-0 + 24-5 



2 



= 22-3 ml ph. 



22-3 X 1609 ^ ^ 

^^ — 36oor- = ^'^ ^ P^- 

The average output per motor is equal to — 

^^'^ ^ ^^^ X 9-9 X 9-81 = 91,800 watts. 

o 

The average current input per motor is equal to — 

91,800 



0-80 X 600 



= 191 amperes. 



Making similar calculations for the average current input for each 
successive 5 seconds, the results set forth in column H of Table XLVII. 
are obtained, and these values are plotted in Fig. 67, which accordingly 
gives the current flowing to each motor from the first instant of 
starting up to the end of the 80th second, i.e. up to the moment 
when the supply of electricity is cut off. 



POWER CURVES 



137 



-4 
in 

B 

O 
H 

Q 
O 

EH 

O 



W 
o 

<j 

o 

EH 

H 
P 

Ph 
*A 
M 

« 
P 

o 

W 

EH 

O 
O 

l-H 
EH 

-4 



H 



PQ 

EH 





Total 

input to 

train 

(kw). 


r-T 


oOrHOocorHiowscNajaDcD-* 

THOCOCNlOCNrHCOt-COOCDO 




Tgtal 

output from 

all motors 

(kw). 


05 


-*OiTH03(MCOiHOOQO»OTj1COT-H 
C0OO05-*iHiH00t-t-t-t~t- 
t-CO»OTHTHTjlTi1COCOCOCOCOCO 




1 

1 

I 


Total 
current to 

train 
(amperes). 


00 
tH 


co^cDoooqcDoooocMOt-co 

CNCOO'^Cqt~iOOC»QOOOt~t- 
O^CN^O 05 CXJOOCKt-t't-t-t- 
rH'T-TT-TT-T 






Current 
input per 

motor 
(amperes). 


CO 


b- »0 iH CO 

iHOOCNOOCftb-THODt-t-b-cb 
01iOCOCOiHOOOOlOiOlO>05 
i-irHrHrHrHrHTHrH 




Output of 

each motor 

(watts). 




8 

cxT 

tH 


OOOOOQOOOOOOO 

0000000000000 
Qq_ th_ 0^ »o^ (W iH^ »q_ »o^ oi^ 05^ 00^ CO_^ rji^ 

T-T co" co" oT lo" cq" rn" od" b-^ co" to" CD*" co" 

05t~CDCDOiO»OrHTJlTilrJ<rHT:t< 




u. 


60 

a 

00 




as 


OlCpODb-THpcpTHCpTH'^cprH 

d^THoqdb-^vbocbcbt-t-t-ci) 




•a 

a 




6 
cq 


CpOCpcpC0b-cpTHTH»H05C0cp 

cqcboooo5cb»ocbt-aocb650 

CMCNCNCOCOCOCOCOCOCOCOCO'«*< 




UJ 


Tractive 

force 

per motor 

(kg per ton). 


8 

05 


iHCO»OOi-ICOtJ<»OCOCDCOOOtH 
OT-rtiCOtHCOOTCqcpOiCpGOt-t- 

cbrficbcbcqcqcqcq^H^iHtHiH 




Q 


Total 
tractive 

force 

(including 

friction) 

(kg per ton). 


OS 


»Ot-00CX)O5O5OSTHrHOib-CqOi 

o»bt-THo6ot-cb>b'*4H'^cb 

OCOCN(MOlTHr-ltHTHiHT-<iHTH 







Mean 

acceleration 
during 
interval 

(ml ph ps). 



CO 
CO 


oooooooooowcoo 

OOTt(Q0OC0T*1iH05Q0t-C0C0 
O5CD-<*0OCOCMCqC?q»-(THTHrHtH 

6666006060600 




m 


Increase in 

speed 

(ml ph). 


6 
3i 


oooooookooot- coo 
opoqgiipopcNpgiOiqpcpco 

'^cb(?qTHiHTHTHtH66666 




< 


03 
> 

a 


QD 
T3 

i 
o 


° flOOO»00»00»00»00»00 
rcJ 0<MCqCOCO-^'<*i»0»OCDlX)t-t-C30 

^olilllllllllll 
S <B»00»0000»00»00»00>0 
** iMrH(MCMOOCOTHTji»OOtOCOt-t- 





138 



ELECTRIC TRAINS 



Out of the first 15 seconds, however, the motors were, for the 
first 7*5 seconds, arranged in four groups, each consisting of two 
motors in series, as shown in Fig. 68. 

During the succeeding 7*5 seconds they were arranged in eight 
parallel branches, as shown in Fig. 69. 

This is termed "series-parallel control," and serves to improve 
the efficiency during starting, since the rheostatic loss during the 



Z9U 






























240 

220 

200 

^ 160 

^ I<a0 




































I 




























\ 




























\ 


L 
























V 

\ JOO 
60 
60 
40 
20 






V 




























\ 


V 




























s 



































































































































































ZO 40 eO 80/00/20 /-A? 

77/na /n Seconds 

Fig. 67. — Current Input to each Motor for the Run indicated in Fig. 66. 



first 7*5 seconds would be much greater were the entire eight motors 
all in parallel from the start. 

The average current to each motor being approximately constant 
during the first 15 seconds, it follows that the total current supplied 
to the train while the motors are in series must be half that supplied 
when the motors are in parallel. We can therefore set down the 
average current input to the train at (246 X 8 =)1968 amperes 
while the motors are in parallel, and 984 amperes while they are in 
series. 

When the motors are running on the motor curve, connected 
right across the 600-volt line without rheostats in circuit, the current 
input to the train is, of course, eight times that to each motor. The 



POWER CURVES 



139 




yari^h/e /fe^/sC^nce cut oi/t 
at ^S.sec /ro/rt Sdar^ tYheA 
Connecdions aire ch^inged ^ 



Fig. 68.— Representation of Series Arrangement of the|8 Motors on the Train. 




out M /^ sec /rom ^L^ 



Fig. 69. — Representation of Parallel Arrangement of the 8 Motors on the Train. 



140 



ELECTRIC TRAINS 



2200 



^2000 




20 -*? 60 ao loo /20 /^ 
77me /n ^conds 

Fig. 70. — Current Input to the Entire Train for tlie Run Indicated in Fig. 66. 



tJUW 

/2O0 

/lOO 

• ^000 

*^dOO 

-5 
























































































\ 




























\ 






























V 






























\ 


V 






















2^ Kn/\ 








\ 






















<iiOO0 

I 

•\400 














— 












































20c 

/oo 























































































20 ^ (30 60 /oo 



/20 



/40 



Fig. 71.— Kilowatts Input to Train for the Bun Indicated in Fig. 66. 



POWER CURVES 



141 



Meat h^eie 



//I /'Sbdc/v =23% '^ 

■A 






values are given in Fig. 70, plotted from column J, Table XL VII. 
The input to the train at any instant can be obtained by multiply- 
ing the corresponding values of the current by 600, the pressure 
in volts, or by estimating from the output of each motor at the 
assumed efficiency. Since the cur- 
rent input to the train during the 
"series" period was one half that 
for the " parallel " period, the power 
input to the train will vary in a 
similar manner, and we obtain the 
curve of total input to the train as 
plotted in Fig. 71. 

By integrating this curve we 
obtain 50,000 kw seconds, which 
reduces to 93 w hr per ton-mile. 
This is 4 per cent, less than the 
97 w hr obtained from Fig. 45, for 
the same schedule, and the dis- 
crepancy is due to taking the value 
of 80 per cent, as the efficiency 
throughout, whereas had this figure 

/93 \ 

been taken at (^ X 80 = )76'7 — or 

say 77 — per cent., the two values 
for the energy consumption would 
have agreed; 77 per cent, is con- 
sequently the average efficiency of 
the motor taken over the entire 80 
seconds from the start up to cut off. 

Thus the total loss in the motors 
must be (100 - 77 =)23 per cent, 
of the total input. This leaves 
(30 - 23 = )7 per cent, for rheostatic 

loss, since the over-all efficiency ^^ ^jf 1 a » ,r\j^m 

the electrical equipment has been n'Me /frea represents /00/> 
assumed as 70 per cent. These 
different losses are shown in Fig. 72 
as percentages of the total input. 

Eeturning to Fig. 67, the curved 
portion gives us data for calculating 
the "speed-curve" of the motor which we require. This portion 
is reproduced in Fig. 73, in which is also drawn a curve of the train 
speed in ml ph taken from Fig. 66. 

From the curves in the above figure we may construct the curve 
in Fig. 74, with speed in ml ph as ordinates and current in amperes 



£A9er^ de//Vr£recf 
^/ro/77 flfoCors Co 
A/e3 - 70% 



Fig. 72. — Showing Allocation of the 
Energy Input of the Run Indi- 
cated in Fig. 66, with an Over-all 
Efficiency of Electrical Equipment 
of 70 per cent. 



142 



ELECTRIC TRAINS 



260 
220 




1 






















































































50 


200 
\tdO 
































' ' 










1 
















40^ 


^ 100 






V 




^ 

^ 


^ 


















*\,l^0 






\ 


X^ 


X^' 




















% 

50\ 

20 


\/00 






/ 


s 


^-^ 


Q., 


'^^-^IJ 


^ 
















/ 


























60 
60 
40 
20 


























































10 


































































TFme 





3eci 


i 



r 


<9 


:? 


/c 


10 


/20 







Fig. 73. — Current and Speed-Curves, re-plotted from Figs. 66 and 67. 



50 


























































40 

% 

% 30 










\ 




























\ 


\ 




























\ 


s_ 




























N 


v^ 














^20 

V5^ 


















^^ 


■^ 


-^ 


^^_^ 


































iO 

























































































/90 60 /20 /eo 200 240 

Current in ^/rtperes j£>er P7odor 

Fig. 74. — Characteristic (ml ph) Speed-Curve of the Train obtained from Fig, 73. 



POWER CURVES 



H3 



as abscissae. This is done by taking pairs of readings on both curves 
for various times. With the data that the car wheel diameter is 
1000 mm, and that the ratio of gearing is 2*47, we can now plot 
another curve as in Fig. 75, with the speed of the motor in rpm as 
ordinates and with the current in amperes as abscissae. 




40 dO /20 /60 200 2^ 

Current per Ahdor /n /Imperes . 



^O 



Fig. 75. — Characteristic (rpm) Speed-Curve of the Motors. 

The values for these conversions are set forth in Table XLVIII., 
together with the calculations for obtaining the successive curves. 



Table XLVIII. — Debivation of the Motor Speed-Curve. 



Time 
(seconds). 


Current input 
to motor 
(amperes). 


Corresponding 

speed 

(ml ph). 


Speed 
(meters p min). 


Circumference 
of driving 

wheel 
(meters). 


Speed of 
wheel 
(rpm). 


Speed of 

armature 

(rpm). 


15 


246 


20-0 


536 


\ / 


171 


422 


18 


182 


23-2 


622 


198 


489 


20 


166 


24-3 


652 




208 


514 


25 


142 


27-0 


725 




230 


568 


30 


128 


29-2 


784 


314 


250 


618 


40 


112 


32-7 


877 


280 


692 


50 


104 


35-7 


957 




304 


750 


60 


98-0 


37-8 


1014 




323 


798 


70 


96-5 


39-5 


1060 




338 


835 


80 


960 


41-0 


1100 


1 


350 


865 



144 ELECTRIC TRAINS 

Having obtained the speed-curve required, we can specify a motor 
of the rated hp required, i.e. 170 (see p. 133), and with a speed-curve 
approximating to that of Fig. 75. Such a motor is suited to the 
conditions of the run indicated in Fig. 66. 

To determine the form of the " motor characteristic " in a speed-time 
diagram when the speed-curve (as Fig. 75) for the motors employed 
is given, the process above described is reversed. For a particular 
speed the current in amperes is obtained from the curve, hence at 
600 volts the input in watts is known, and the watts output is then 
derived on multiplying by the known efficiency of the motor for the 
load in question. The output in kg m ps is next obtained by multi- 
plying by 9*81 (since 9*81 w equal 1 kg m ps). Then, dividing the 
figure for kg m ps by the corresponding speed in m ps, the total 
available effort in kg is determined, and from this the kg per ton of 
train. Then, subtracting 6 kg per ton for the friction component, 
the accelerating force and acceleration are found, corresponding to 
the speed taken. 

By assuming a time interval of 5 seconds, the change in speed 
produced by this acceleration is deduced, giving two points on the 
speed-time diagram. With the second speed obtained, the amperes 
are again looked up from the curve and the operations repeated. 

The calculation is best done tabularly, similarly to Table XL VII., 
and the complete speed- time " motor curve " can then be drawn. 



CHAPTER XI 

THE HETSEAM, MORECAMBE AND LANCASTER ELECTRIFIED 
SECTION OF THE MIDLAND RAILWAY. 

The pressure limitations of electrical equipment with continuous 
motors have led to endeavours to apply alternating motors to train 
propulsion. Both polyphase and single-phase motors have been 



nxecambe 



" "f i '* ' 



/\ ' tOmI fjl limit 
B- fS 





ffhiss 

trSta 

IgnatjicrOii 



Fig. 76. — Plan of Electrified Section of Midland Railway at Heysham. 



successfully employed on railways. In England motors of the 
single-phase type are the only alternating motors which have as 

145 L 



146 



ELECTRIC TRAINS 



Hey shun OockSta — 



^ 



PHiJt/fcton ^oiJ - 



Tornsholme JunC:lio.2r 



Toms holme June tia.tr 
Torrisfiolme Junc.ft9.Zr 



— ^ 



Hest Bank June 
Morecambe 5 (J 



He si Ba.nfr June for. 
Hey shim di'^nch 



Tornsholme June No L 



iancister Sts 




e3 



a 

i-H 



o 

CO 

cd 



pq 






O) 

o 

«f-l 

o 

c3 
e3 



M 
1^ 



yet been used. Since, so far as regards 
energy consumption at the train per 
ton-mile, single-phase equipments are 
about on a par with continuous equip- 
ments there has been no occasion 
to discuss systems in the preceding 
chapters, since these have dealt mainly 
with energy consumption. Further- 
more, the wealth of available data 
relating to undertakings employing con- 
tinuous equipments has made it con- 
venient to base descriptions on the 
continuous system. There are, however, 
very important distinctions between the 
characteristics of trains, according as 
they are equipped with continuous or 
single-phase apparatus, and it is desir- 
able at this point in the treatise to 
introduce data relating to single-phase 
trains. 

The first single-phase trains operated 
in England are those employed on the 
Heysham, Morecambe and Lancaster 
section of the Midland Kail way, where 
a trolley pressure of 6600 volts is used 
at a periodicity of 25 cycles. A plan 
of the electrified system is given in 
Fig. 76. In Fig. 77 the route is de- 
veloped along a straight line, below 
which are indicated the gradients and 
curves. To obtain a broad grasp of the 
plan, we may consider a train operating 
between Heysham and Lancaster, and 
making an intermediate stop at More- 
cambe. Thus we have a route of 8*1 
miles with one intermediate stop. Since 
Morecambe, the intermediate station, is 
4' 7 miles from Heysham and 3 '4 miles 
from Lancaster, the average distance 
between stops is 4*05 miles. For our 
purposes we may round this off to 4*00 
miles. A good many curves relating 
to the performance of trains operated 
over this route have been published, 
but unfortunately there are serious 



HEYSHAM AND MORECAMBE ELECTRIFICATION 147 

evidences of inaccuracy in them. Thus, in a paper by Dalziel 
and Sayers, read on November 9, 1909, before the Institution 
of Civil Engineers (vol. clxxix. pt. L, p. 47), there are published 
four speed-time diagrams relating to runs between Morecambe and 
Heysham. I have integrated these four speed-time diagrams, and 
the distance works out in the four cases at 4* 77 miles, 3 '84 miles, 
4" 5 9 miles and 4* 16 miles. The mean of these four results is 4*3 
miles, the individual results being respectively 11 per cent., 12 
per cent., 7 per cent., and 5 per cent, different from the mean. The 
largest result is no less than 26 per cent, greater than the smallest 
result. Similarly, two of the curves relating to runs between More- 
cambe and Lancaster lead to utterly different results as regards the 
distance between these two stations. Notwithstanding these dis- 
concerting evidences of inaccuracy, it may, nevertheless, be of interest 
to examine the rough results obtained as regards the energy consump- 
tion of a train weighing 80*5 tons and operated over this route. The 
data is given in Table XLIX. — 



Table XLIX.— Energy Consumption of Tbains on the Heysham Section 

OF the Midland Railway. 



Section, 


Distance (miles). 


Time (seconds). 


Train consump- 
tion (whr). 


Average speed 
(ml ph). 


Heysham to Morecambe 
Morecambe to Lancaster 
Lancaster to Morecambe 
Morecambe to Heysham 


4.7 
3-4 
3-4 
4-7 


600 
368 
417 
451 


13,050 
11,800 
11,900 
16,050 


33-8 
33-2 
29-4 
37-5 


Total 


16-2 


1786 
= 28-9 min 


52,800 


33-6 



Of course, in practice the train conforms to a time-table adapted 
to the conditions of the traffic, which involves the times of arrival 
and departure of steam boats and steam trains. It is only for purposes 
of a rough but instructive examination of the undertaking that these 
four test runs have been so brought together, as in Table XLIX,, as 
to constitute a complete round trip. If this round trip were main- 
tained, and if at each station a 30-second stop were made, then the 
time, including stops, would be — 

1736 -h 4 X 30 = 1856 seconds 
(or 28-9 +4x0-5 = 30*9 minutes). 



148 ELECTRIC TRAINS 

The schedule speed would then be — 

1736 



1856 



X 33-6 = 31-4 ml ph. 



Per round trip of 16*2 miles there are accomplished 16*2 train-miles, 
and — 

16-2 X 80-5 = 1300 ton-miles. 

Consequently, the energy consumption at the train works out at — 

52,800 



1300 



= 40*5 w hr per ton-mile. 



Turning to Fig. 45, on p. 80, we find that for a schedule speed of 31*4 
ml ph, with a stop every 4*00 miles, the energy consumption is given 
as about 38 w hr per ton-mile. The agreement is thus within 7 per 
cent., and it may be said that consistent values are gradually emerging 
from the sporadic tests being made in various parts of the world, and 
corresponding to various services. It is hardly justifiable to attempt 
to explain so small a divergence as 7 per cent., as it constitutes agree- 
ment rather than disagreement. It can, however, be partly accounted 
for by the frequency of sharp curves on the route, and the necessity 
of slowing down at some of them. 

The electrical equipment comprised two 180-hp motors and the 
requisite auxiliary apparatus. Thus we have — 



Rated capacity of equipment . 
Consumption per ton-mile (a) 
Weight of train . • (^) 
Consumption per train-mile (c = a x h) 
Schedule speed . - (d) 

Average input . . (e = c x d) 



360 hp 
40*5 w hr 
80-5 tons 
3260 w hr 
31-4 ml ph 
102,000 watts 



From tests given later in this chapter (see p. 154) an appropriate 
value for the efficiency of the equipment under these conditions of 
service is seen to be some 72 per cent. 

/. Average output (/ = e x 0*72) . . . 73,500 watts 
„ (/4-746) . . . . 98hp 
„ „ per motor . . r . 49 hp 

„ „ intermsofratedoutputof motor 27*2 per cent. 

As a matter of fact, the actual service is much less severe than 
this. Thus, it was specified that the motors should run an 80*5-ton 
train (one motor-coach and two trailers) for six complete double 
trips, allotting 20 minutes to the round trip between Morecambe 
and Heysham, and 15 minutes to the round trip between Morecambe 
and Lancaster. It would thus appear that 35 minutes would be 



HEYSHAM AND MORECAMBE ELECTRIFICATION 149 

allotted to a complete round trip between Hey sham and Lancaster, 
intermediate stops being made at Morecambe. But in the above 
analysis only 30*9 minutes were allotted to this round trip. 
Assuming that the additional 4*1 minutes is devoted to stops at 
stations, then the energy consumption remains at the figure already 
worked out, but the schedule speed falls to — 

^ X 31-4 = 27-7 ml ph 
00 

as an average for the (35 X 6 =)210 minutes (3*5 hours) occupied 
in running the six complete double trips specified. Thus, the average 

/30*9 \ 

load was I-oH" ^ ^'^'^ "^ )24 P®^ c®^^- ^^ rated load, and practically 

conforms with the established practice on London's underground 
tube railways. Nevertheless, the motors are cooled by forced draught, 
the provision of which requires an average consumption of 750 watts 
per train, or 0*75 of one per cent, of the average input to the train. 
Moreover, the motors alone (including gear and gear case) weigh 3-12 
tons each, or 17"3 kg per rated hp, whereas the C.L.E. motors 
(described in Chapter VI.) only weigh 1-96 tons each, or 15 '9 kg per 
rated hp. On the G.N. P. and B. railway the G.E.69B motors employed 
(see Chapter VII.) have a 1-hour, 75° C. rating of 240 hp and weigh 
2'80 toDS each, or 11*7 kg per rated hp. No forced draught is employed 
with these continuous equipments. Taking the complete equipment 
in the three cases the weights are — 

Weight of complete 
electrical equipment 
Railway. per 1-hour, 75° C. rated hp. 

Central London . . 20-0 kg 

Great Northern Piccadilly and Brompton .... 15-4 kg 
Heysham, Morecambe and Lancaster (Siemens' equipments) . 40-7 kg 

It will be found characteristic of single-phase railway equipments 
that their weight per hp is of the order of twice that of continuous 
equipments. The G.E.69B motor of the G.N.P. and B. railway is 
sold as of only 200-hp rating, being very conservatively rated, but 
even if taken on this basis, instead of on the 1-hour, 75° C. basis, the 

weight of total electrical equipment is only ( otjtv X 15'4 = )l8*5 kg 

per hp, as against 40*7 kg per hp for the Siemens single-phase 
equipments employed at Heysham. On the other hand, although the 
Siemens motors were sold as of 180-hp rated capacity, it is stated to 
have since been demonstrated that they rate at this output, having 
only 75° C. rise at the end of one hour, without resorting to forced 
ventilation, and that with forced ventilation they rate at 210 hp. 
Thus, comparing the forced-ventilated Siemens motors as of 210 hp, 



I50 ELECTRIC TRAINS 

with the G.E.69B motors, without forced ventilation, as of 200 hp, 
then the respective values are as follows — 



Type. 


Eating. 


Weight of complete 
equipment per hp (kg). 


Siemens (forced ventilation) 
G.E.69B (natural ventilation) . 


210 
200 


35-0 
18-5 



On this basis the single-phase equipment weighs — 
(lH ^ 1'89)89 per cent. 

more than the continuous equipment. It should also be pointed 
out that whereas at their rated load the G.E.69B motors have a speed 
of only 530 rpm, the speed of these Heysham motors at their rated 
load is 770 rpm, i.e. 45 per cent, greater, and, nevertheless, their 
weight per rated hp is much greater. 

With this preliminary sketch of the nature and purpose of the 
system, the reader will be in a position to read with some interest a 
descriptive account of the apparatus and of the trains on which it is 
installed. 

The rolling stock consists of three trains, each consisting of three 
coaches. There are three motor-coaches, two with equipments by 
Messrs. Siemens Brothers, and one equipped by the British Westing- 
house Company. The remainder of the rolling stock consists of 
trailer-coaches. Each end of each of the motor-coaches and trailer- 
coaches is provided with control apparatus. This provision is made 
in order that the length of the trains may be varied to suit the traffic, 
which varies from season to season. The coaches are repeatedly 
reversed at the triangular junction at Morecambe. 

A specification of both the Siemens and Westinghouse motor- 
coaches, the trailer-coaches, and of a typical 3-coach train, are given 
in Table L. 

Table L. — Specification of Electbic Trains on Midland Eailway (Heysham, 
Morecambe and Lancaster Branch). 

A. — Motor-Goach. B. — Trailer-Coach. C. — Complete Train. 

A. — Motor-Coach. 

General — Siemens. Westinghouse. 

Total length over end panels 60 ft 60 ft 

Length of passenger compartment .... 52 ft — 

Composed of three divisions, the centre one 25 ft in length, transverse seats, and 
two divisions 13 ft 5 ins with longitudinal seats. 

Height, over-all, above rail level . . . . 12 ft 9 ins 12 ft 9 ins 

Width, over-all, outside 9 ft 9 ft 

Seating capacity ....... 72 72 



HEYSHAM AND MORECAMBE ELECTRIFICATION 151 



Weight of coach without passengers 

,, of coach body, including under-frame, air 

compressors, seats, upholstering, and all fittings . 

Seats per foot length of coach .... 

„ ton weight of coach ..... 

Weight per seat ....... 

Trucks and Bogies — 

Weight of motor bogie without motor 
Wheel base of motor truck 

,, of trailing truck . 

Axle diameter, mid frame (motor bogie) 

„ ,, at bearing 

Length of bearing .... 
Diameter of driving wheels (new) 
Gauge of track .... 

Electrical Equipment — 

Rated hp . . . . . 
Pressure in volts .... 

Method of control: multiple unit, the i 
system," while the Westinghouse has the electro-pneumatic system 

Gear ratio ........ 

Weight of one motor alone ..... 
,, of motor and gear ..... 

Motors per motor-coach ...... 

Total weight of motors with gearing per motor-coach 

Weight of balance of electrical equipment (i.e. con- 
trollers, transformer, rheostats, etc.) per motor- 
coach ......... 

Total weight of electrical equipment per motor-coach 

Batio of total weight of electrical equipment to weight 
of motors and gearing ...... 

Weight of motor in kg per hp (rated) 

,, of motor and gear in kg per hp . 
,, of all electrical equipment in kg per ton 
weight of motor-coach ...... 368 

Ratio of total weight of electrical equipment to 
weight of motor-coach . ..... 037 



Siemens. 


Westinghouse. 


40'5 tons 


37-5 tons 


15-1 


14-9 


1-2 


1-2 


1-78 


1-92 


0-56 tons 


0-52 tons 


6'5 tons 


6-5 tons 


8 ft 6 ins 


8 ft 6 ins 


8 ft 


8 ft 


6^ ins 


— 


4| ins 


— 


9 ins 


— 


3 ft 7| ins 


— 


4 ft 8^ ins 


— 


180 


150 


340 


235 


having the 


" all-electric 


c system. 




2-9 


3-9 


2-8 


2-5 


812 


2-78 


2 


2 


6-25 tons 


6'55 tons 


8-65 


6-8 


14-9 


12-4 


2-38 


2-22 


15-5 


16-8 


17-3 


18-7 



330 



0-33 



B. — Trailer-Coach. 



Length, over-all 

Height, over-all, above rail level 

Width, over-all, outside . 

Seating capacity 

Total weight of trailer-coach . 



C. — Complete 3-Coach Train. 



Number of motor-coaches 
,, of trailer-coaches 
Total length of train 
Weight of motor-coach component 
„ of trailer-coach component 
Total weight of train without passengers 
Seating capacity .... 
Number of motors per train 



43 ft 




13 ft 




9 ft 




54 




17'5 tons 




1 


T 


2 


2 


150 ft 


150 ft 


40-5 


37-5 


36 


36 


77 tons 


74 tons 


180 


180 


2 


2 



152 ELECTRIC TRAINS 

Siemens. Westlnghouse. 

Total hp of train 360 300 

,, weight of motors and gearing. . . . 6*25 tons 5-55 tons 

„ „ of electrical equipment . . . li'Q „ 12*4 ,, 

Rated hp per ton of train ..... 4*68 4-05 

„ per seat of train ..... 2*00 1-67 
Total weight of motors and gearing in kg per ton of 

train 82-5 76-2 

Total weight of motors and gearing in kg per seat of 

train 35-2 31-2 

Total weight of electrical equipment in kg per ton of 

train 197 170 

Total weight of electrical equipment in kg per seat 

of train 83-6 69-5 

Ratio of total weight of electrical equipment to total 

train weight 0-197 0*170 

The braking equipment is of the combined power (vacuum) and hand type, 

A photograph of a Siemens motor-coach complete is shown in Fig. 
78, and of the Westinghouse motor-coach in Fig. 79. A standard 
3-coach train hauled hy a Siemens motor-coach is shown in 
Fig. 80. 

The train specification issued by the engineers of the Midland 
Eailway Company, called for two motors per motor-coach, to be 
carried on one bogie. Thus each motor- coach comprises a motor 
bogie and a bogie without motors. The normal train was 
specified to consist of one motor-coach and two trailers, the motor- 
coach seating 72 passengers and the two trailers to each seat 54 
passengers, thus providing 180 seats per train of three coaches. 

It will be seen from Fig. 77 that the route embodies several sharp 
curves. The speed of the train is restricted to 15 ml ph at these 
curves, and in some instances to 10 ml ph. The contractors were 
called upon to supply trains capable, under these conditions, of 
maintaining a 20-minute service between Heysham and Morecambe 
with a single train, and a 15-minute service between Morecambe 
and Lancaster. It was required that the motor-coach should be of 
such capacity as to enable it on occasions to haul two additional 
standard Midland Eailway coaches, each weighing 26 tons, bringing 
up the total train weight to some 125 to 130 tons. This train was 
to be capable of climbing the gradient of 1 in 70 existing on the 
short, single-track branch line between Lancaster Green Ayre 
Station and Lancaster Castle Station. 

To meet these conditions, Messrs. Siemens Bros, equipped 
their two motor-coaches with two 180-hp motors per coach, 
and the Westinghouse Co. equipped their motor-coach with two 
150-hp motors. The specification required that the motors were 
to be capable of delivering, when tested on the stand with single- 
phase electricity and at the specified periodicity of 25 cycles per 
second, their declared output for one hour with a temperature 




Fig. 78. — Siemens Motor-Coach. Complete. 
{Heysham Branch of tlie Midland Rallivay.) 




Fig. 79. — Westinghouse Motor-Coach Complete. 
{Heysham Branch of the Midland Railway.) 




Fig. 80. — View of Train consisting of Siemens Motor-Coach and Two Trailers. 
{Heysham Branch of the Midland RaiUray.) 

\_Toface p. 152. 



HEYSHAM AND MORECAMBE ELECTRIFICATION 153 

rise not exceeding 135° F. (57'2° C.) above the surrounding air. 
They were also required to have a temperature rise not exceeding 
90° F. (32*2° C.) after hauling the three-coach train for six double 
trips at the schedule mentioned above, from Heysham to Morecambe, 
Morecambe to Lancaster and return. Six such trips, however, only 
correspond to carrying 24 per cent, of the rated load of the motors for 
three and one-half hours. 

The 20-minute service between Heysham and Morecambe requires 
that the train shall perform the single journey in about 500 seconds 
from start to stop, the train making on an average 6 journeys either 



0U 
















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L. 
































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2CX) 

/7me 



3CO 



-400 



seconds . 

Fig. 81. — Speed-Time Diagram for 3-43-miles Bun at an Average Speed of 33'3 ml ph. 



way in each hour. The distance is about 4*7 miles, and thus the 
train performs its trip at an average speed of some 

^J^ X 4-7 = 33-8 ml ph. 
oUO 

Between Morecambe and Lancaster the time taken by a train per 
trip is about 400 seconds, there being 8 such trips in each hour. The 
average speed thus amounts to about — 

?^ X 3-4 = 30-6 ml ph. 
400 

For so long a run, the speed-time diagram is less definite than 
that for the short runs which we have considered in previous 
chapters. Nevertheless, the speed- time diagram of Fig. 81 has been 



154 ELECTRIC TRAINS 

drawn as a mean of Figs. 25 and 27 of Dalziel and Sayers' original 
paper, in order to form a basis for analysis, these figures representing 
runs between Morecambe and Lancaster and between Lancaster and 
Morecambe respectively. 

The estimation shown in Table LI. is based on the speed-time 
diagram of Fig. 81. 

Table LI. — Analysis of Tests on the Midland Trains. 

Distance from start to stop ........ 3*4:3 miles 

Time from start to stop 373 seconds 

Average speed start to stop . . . . . . , 33"3 ml ph 

Assumed duration of stop for a hypothetical schedule . . .60 seconds 

Schedule speed .......... 28*7 ml ph 

Crest speed ........... 52*5 ml ph 

Momentum per ton at crest speed = 0*0278 x 1*09 x V- , . . 83*5 w hr 

,, ,, ton-mile ......... 24*2 w hr 

Assumed tractive force per ton for train friction. (This is taken lower 
than for runs with frequent stops, as in accordance with experience, 
and more especially because in this case only two out of 12 axles 

carry gears) . . . . . . . . . . 4 kg 

Time electricity is on ........ . 152 seconds 

Mean speed during this time . . . . . . . . 32 ml ph 

Distance covered during this time ....... 1*35 miles 

Train friction per ton while electricity is on . . . . . 8700 kg m 

„ in w hr . . . 123*6 w hr 

„ per ton-mile. ........ 6*9 w hr 

Input per ton-mile allocated to momentum and friction . . . 31*1 w hr 

Total input per ton-mile ......... 43*2 w hr 

Balance to be accounted for as loss in the electricity equipment . 12*1 w hr 

Efficiency of electrical equipment as thus estimated . . , .72 per cent. 

The train weighed 80*5 tons, and comprised 3 coaches, of which 
one was a Siemens motor-coach weighing 40*5 tons. The remaining 
(80*5 — 40*5 =)40 tons was made up of two trailers and the load. 

The 40*5 tons weight of the Siemens motor-coach was made up 
as follows — 

Motors with gear, gear-case, and suspension-bar . . 6*25 

Main transformer ........ 2*725 

Auxiliary commutating transformer and preventive coil . 0*975 

Pumps and compressors ....... 0*475 

Contactors and chambers . . . . . . 1"125 

Other sundries, including bows, blowers, controllers, 

cables, etc 3"35 

14-9 

Coach-body 13*25 

Special supports . . 1*3 

Coach-bogie ......... 4*5 

Motor-bogie 6*55 

40*5 



HEYSHAM AND MORECAMBE ELECTRIFICATION 155 



Let us now continue the tabular calculation of Table LI — 



Input per ton-mile 
„ „ train-mile 

Average input per train = 



3480 X 28-7 



1000 

„ „ motor : . . . 

„ output per motor = 36 kw = 

„ in per cent, of rated output of 180 hp 

„ output per motor during the time elec- 

^ . .^ . 373 + 60 ._^ 

tricity IS on = — zr-^ — ^ 4^*2 = • 



5001 






xo 



wo 



DO 






eoo 



600 



^ttO 



200 



43-2 w hr 
3480 w hr 

100 kw. 

50 kw 
48-2 hp 
26*8 per cent. 

137 hp 



230 












































































































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77mc in 'Seconds • 
Fig. 82. — Curves relating to the Energy Input for the Eun indicated in Fig. 81. 



156 



ELECTRIC TRAINS 



In Fig. 82 are given the curves of pressure and current per motor 
during the 152 seconds that electricity is on, as also of the values of 
the kw input and the power-factor during the run. 

The characteristic curves of the motor, as obtained on factory 
tests, are shown in Fig. 83. 

In both the Siemens and Westinghouse motor-coaches the motors 
are provided with forced draught. For the Siemens motor-coach the 
suction duct has been carried inside the coach under one of the seats, 
the whole of the air coming in this case from the inside of the coach. 
The Westinghouse motor-coach has a similar duct inside, but there 
is also provided a suction duct with a filter taking air from outside 



tCOD 



\4000 



2000 




200 ^W WO Wd 

Current Input in Anp 



iVO -«V too SOO 

Currvnt JnpuC in ^/np. 



Fig. 83. — Characteristic Curves of the Siemens Motor on the Heysham Electrified 

Portion of the Midland Railway. 



the coach. The power required by the fan motor is 1*5 kw in the 
Westinghouse, and 0*75 kw in the Siemens coach. The tests of the 
Siemens motor at the makers' works, with forced draught and with 
300 volts at the terminals (the full pressure being 340 volts), is 
stated to have indicated that they were capable of sustaining 
210 hp for one hour without exceeding their guaranteed temperature- 
rise. It is also stated that the motors were capable of developing 
150 hp at full pressure and with a forced draught that requires about 
1-5 kw for the fan, without exceeding their guaranteed temperature 
rise. 

The weight of the Westinghouse motor-coach is 37*5 ton, this 
weight being made up as follows (weights are given in tons) : — 



HEYSHAM AND MORECAMBE ELECTRIFICATION 157 



Motors with gear, gear-case, and suspension bar . 

Main transformer 

Auxiliary commutating transformer and preventive coil 

Pumps and compressors 

Contactors and chambers ...... 

Other sundries, including bows, blowers, controllers, cables, 
etc. 



Coach-body 
Special supports . 
Coach-bogie 
Motor- bogie 



Total 



5-55 
2-55 
0-47 
0-80 
0-49 

2-49 

12-35 

13-25 

0-85 
4-50 
6-55 

2515 

37 5 



I 



The Hey sham electrified section of the Midland Railway has been 
described in detail in a great many articles in technical journals and 
in papers read before various institutions. To these articles and 
papers the reader is referred for more complete details, not only of 
the electrical equipment of the coaches, but also of the overhead 
construction, power station, etc. For this purpose I have brought 
together the following references : — 

1. Electrical Engineering, for June 11 and 18, 1909. 

2. Electrician, for June 12 and 19, 1908. 

3. Railway Gazette, for June 12 and 19, 1908. 

4. Engineer, for June 12 and 19, 1908. 

5. Electrical Review, for June 12 and 19, 1908. 

6. Light Railway and Tramway Journal, for June 5, 1908. 

7. Journal Institution of Electrical Engineers. Paper on " Single- 
Phase Railways," by Percy C. Jones, vol. 43, p. 723. 

8. Proceedings of the Institution of Civil Engineers, vol. clxxix. 
pt. 1, p. 31. " The Single-Phase Electrification of the 
Hey sham, Morecambe and Lancaster Branch of the Mid- 
land Railway," J. Dalziel and J. Sayers. 



CHAPTER XII 

THE HEATING OF RAILWAY MOTORS 

A VERY useful comparison of railway motors may be based on a study 
of the watts dissipated in internal motor losses per ton weight of 
motor. This comparison may be made under the conditions of actual 
service and also under the conditions of the 1-hour, 75° C. rating. In 
carrying out such a comparison we must exclude the gear losses, and 
also the weight of the gear and gear case. It is reasonable that the 
results obtained should be quite varied, since they will to a con- 
siderable extent be dependent upon the design of the i motors and 
upon the conditions attending their use in actual service. Never- 
theless, a general knowledge of the order of magnitude of the 
" watts per ton " is of importance. 

Q.E.66A. Motor— Central London Railway 

Let us take, for example, the motor used on the Central London 
Kail way which was considered in Chapter VI. It is rated at 125 hp, 
and from its efficiency curve (curve F of Fig. 52) the efficiency at 
this output, including gear loss, is seen to be 90 per cent. The 
efficiency, exclusive of gearing, is seen to be 93*5 per cent, (curve E of 
Fig. 52). Therefore the gearing loss is some 3*5 per cent. The input 
to the motor at rated load is — 

-^ X 746 = 103,800 watts. 

Output from the armature axle to the gear — 

= 0-935 X 103,800 
= 97,000 watts. 
Internal losses = 103,800 - 97,000 

= 6800 watts. 

The weight of the motor without gear and gear case is 1*75 ton. The 
loss per ton, therefore, amounts to — 

6800 



1-75 

158 



= 3880 watts. 



HEATING OF RAILWAY MOTORS 



159 



Similarly, the internal losses in the motors may be estimated in other 
cases, and three examples are given in Table LII. — 



Table LII. — Values op Internal Losses in Motors at Rated Load. 







(-1 

1 


J3 


3.2 


2 


60 

.S-d 

30 


1- 

if 

si 


2 


|3 






^•y 


t 


s-s 


. 


j1 <i^ 




_ 1 OD 




Motor. 


Railway. 


® a 

■u 


3 


>;s 


-" eS 




2-^ 


S g 


.a^s 






1^^ 







a 






a 
1— 1 


O) 1^ 






^ 


« 


1- 




|S> 


s-S 







G.E. 66A 


Central London 


1-75 


125 


90-0 


103,800 


93-5 


97,000 


6,800 


3,880 


G.E.69B 


Gt. Northern J 
Piccadilly and > 


2-51 


C 200 


88-0 


169,500 


92-0 


156,000 


13,500 


5,390 




Brompton 




\ 240 


87-0 


206,000 


91-0 


187,500 


18,500 


7,370 


Dick- 


Lancashire and 




(1 hr 75°) 














Kerr 


Yorkshire 


2-75 


150 


88-0 


127,000 


92-0 


117,000 


10,000 


3,640 



A representative figure for the watts loss per ton at rated output 
for continuous railway motors is 4500. 

The G.E.69B motor of the G.N.P. and B. Railway is an instance 
of a case where this value is greatly exceeded. The motor is usually 
sold as a 200-hp motor, but on the 1-hour, 75° C. basis, it is rated at 
240 hp. It has openings in the frame protected by perforated covers, 
as shown in Fig. 84, whereas the C.L.R. and the L. and Y. motors 
are completely enclosed. 

In Chapter VI. a series of tests made on the Central London 
Railway were analysed, and we can use the results to study the 
average loss in the motors taken over the period of actual service. 
Certain of the results, as calculated in Chapter YI., Table XXIX., are 
re-stated below. 



Total number of coaches. 



Average load per motor while electricity 
is on (hp) 



56-8 



49-5 



6 


4 


43-4 


35-6 



30-0 



Eef erring to the efficiency curve of Fig. 52, we can read off the 
efficiencies, exclusive of gearing, corresponding to the above loads, 
from the curve E. 

These values are set forth in Table LII I. — 



i6o ELECTRIC TRAINS 

Table LIII. — CAEiCULATiONS for G.L.R. Motor Losses in Service, 



Average load per motor while electricity 
is on (hp) ...... 

Efficiencies, including gear, correspond- 
ing to above loads (from Fig. 52) 

Corresponding input to motor, including 
gear loss (watts) .... 

Estimated efficiency, excluding gear 
(from Fig. 52) 

Average output from the motor to the 
gear (watts) 

Average loss in motor 
is on (hp) . 



while electricity 



Ratio of time electricity is on to the 
total time of each run, including stop 
(see Chapter VI., p. 89) . 

Average loss per motor (watts) taken 
over the whole run of 110 seconds 

Average loss per motor taken over the 
whole running period (watts per ton) . 



56-8 


49-5 


43-4 


35-6 


86-8 


85-5 


84-0 


82-0 


48,930 


43,100 


38,600 


32,400 


94 


94 


94 


93-5 


46,000 


40,510 


36,280 


30,300 


2,930 


2,590 


2,320 


2,100 



30-0 

79-5 
28,190 

93-3 
36,300 

1,890 




The value for the 6-coach train is 046 watts per ton. This is 
only 16*6 per cent, of the 3880 watts per ton, at rated load, as set 
forth in Table LII.* 

G.E.69B. Motor — Great Northern, Piccadilly, 
and Brompton Railway 

The tests on the Great Northern Piccadilly and Brompton line 
which were considered in Chapter VII. may also be analysed in a 
similar way. In Table LII. the values of 5390 watts per ton and 
7370 watts per ton are taken as the loss in the G.E.69B motor when 
rated at 200 hp and 240 hp respectively. 

From Table XXXIII. we have obtained values for the average hp 
output during two test runs. These values are — 



Test. 


A 


B 


Average hp output from each motor during the time 
electricity is supplied 


100 


114 



* While the calculations given in this chapter have considerable interest from 
the standpoint of relative comparisons, the absolute quantitative results for the watts 
per ton under the conditions of service are considerably too low, since they are 
arrived at by employing the efficiencies for the average load when the motors have 
full line pressure at their terminals, whereas actually the motors are for a part of the 
time in series and there is also resistance in circuit. Under these conditions the 
average efficiency of a motor is considerably lower, and its internal loss is conse- 
quently higher, often to the extent of 60 per cent, or more. 



HEATING OF RAILWAY MOTORS 



i6i 



The efficiencies at these loads can be obtained from the curve of 
Fig. 57, and the motor losses may be estimated as shown in Table 










Fig. 84. — G.E.69B Series-wound Continuous Motor. 

One-hour rating = 240 hp 

Weight (including gearing) = 2*8 tons 
Speed at one-hour rating = 530 rpm 



LTV. The weight of the motor, exclusive of gear and gear case, is 
2-51 tons. 



M 



l62 



ELECTRIC TRAINS 



Table LIV. — Calculations op G.N.P. and B. Ely. Motoe Losses in Service. 



Tests. 



Average hp output per motor while in circuit . 
Efficiency of motor (including gear) at the above load, from 

Fig. 57 

Corresponding input to motor, including gear loss (watts) . 
Efficiency of motor, excluding gear ..... 
Corresponding output from motor to gear (watts) 
Average internal loss in motor while electricity is on (watts) 
Time that electricity is on during each run (seconds) 
Total time of running, including 12- second stop (seconds). 
Ratio of the time that motors are in circuit to the whole 

running time ........ 

Average internal loss in watts per motor taken over the 

whole period ........ 

Do. watts per ton of motor 



100 


114 


89 


89-5 


83,900 
93 


95,000 
93-5 


78,000 

5,900 

41 


88,900 

6,100 

44 


110-6 


104-4 


0-37 


0-42 


2,180 
870 


2,540 
1,010 



The mean value gives 940 watts per ton for the internal losses, 
which is only some 13 per cent, of the value at the 240-hp rating, 
and some 17*5 per cent, of the value at the 200-hp rating. 



Lancashire and Yorkshire Railway 

The data given for the Lancashire and Yorkshire Eailway afford 
two further tests, which are given in Table XXIV. The estimated 
average outputs from that Table are as below. 



Test. 


1 


2 


Average hp output per motor while in circuit during the 
test runs shown in Chapter V. 


93 


79 



Let us use the same methods as in the previous cases for estimating 
the motor losses. The motor weighs 2'75 tons, not including 
gear. 

Fig. 43 gives a representative eflSciency curve for a motor of 
150 hp, and similar to the motor employed on the Lancashire and 
Yorkshire Eailway. The curve is quite sufficient for obtaining 
approximately correct results for the motor in question. The calcu- 
lations are set forth in Table LV. 



HEATING OF RAILWAY MOTORS 163 

Table LV. — Calculations of L. & Y. Motor Losses in Service. 



Test. 



Average output per motor while in circuit (hp) 

Efficiency from representative motor efficiency curve G in 

Fig. 43, including gear 

Corresponding input to motor including gear loss (watts) . 
Probable efficiency, excluding gear (from Fig. 43, curve E) 
Corresponding output from motor to gear (watts) 
Internal loss per motor taken over the time while electricity 

is on (watts) ........ 

Ratio of time during which electricity is on to total time 

(Table XXIV.) 

Internal loss per motor averaged over the whole running 

time, including stops (watts) ..... 

Internal loss per motor in watts per ton of motor 



93 


79 


88-5 

78,400 

93 

72,900 


87-5 

67,400 

93 

62,580 


5,500 


4,720 


0-400 


0-519 


2,200 
800 


2,450 
890 



These results give an average of 845 watts per ton of motor 
which is 23*2 per cent, of the value for the rated load. 

Summarising the results we obtain the values given in Table LVI. — 



Table LVI. — Comparison of Motor Losses at Rated Load and during Service. 



Type of 
motor. 



G.E. 66A 
G.E. 69B 



Dick- 
Kerr 



Railway on which 
motor is used. 



Central London 
Gt. Northern 

Piccadilly and 

Brompton 
Lancashire and 

Yorkshire 



, to 

•^ -s 

H 



1-75 
2-51 

2-75 





'3 


"3 ®.S 




<*-> 


CT3 . 


a o OS • 




o 


(-1 a3^~> 


tn 'r^ *« O 






^^H 




«l<j 


1' 


— Average in 
loss at rated 
(watts per t 


B — Average in 

loss during se 

with a Stan dan 

(watts per t 


Percentage 




< 




125 


3880 


646 


16-7 


200 


6390 


940 


17-5 


240 


7370 


940 


12-7 


(1-hr rating) 








150 


3640 


890 


24-5 



« o a u 

-fl =? bob „bo 

• 0? (-4 S -t-a -4^ 

<p oj o -r* o 

^1 a ^ " 



17-3 

21-5 
17-9 



27-3 



The losses of the G.E. 66 A and the Lancashire and Yorkshire motors 
at rated load are around the average figure of 4500 watts per ton, 
which is representative of the internal losses at rated load for 
railway motors with natural ventilation. The percentage which the 
continuous rating of railway motors bears to the 1 hour, 75° rating 
may be anything from 20 to 40 per cent. ; and the figure for the 
totally enclosed type is usually 25 per cent, when it is estimated 
from the average load carried by the motors during service, as per 
cent, of the 1-hour rating. 

The values for the G.E.69B motor depart from the other values, 
but this is due to the design which embodies openings in the case, as 



1 64 ELECTRIC TRAINS 

already described. This gives a high weight efficiency (i.e. a high 
output in hp per ton of motor). The gear loss at rated load was 
taken as 4 per cent., and in this case is the same during service, 
since the curve of Fig. 57 is nearly straight between the values of 
100 and 240 hp. The value for the watts loss per ton during 
service agrees with the other values ; while the high figure for the 
internal loss at rated load necessarily gives a low percentage for the 
value which the loss during service constitutes of this 1-hour rated 
load loss. 

Sing^Ie»phase Motors 

By the use of forced draught the heating of motors may be con- 
siderably reduced for a given weight of motor, or, what amounts to 
the same thing, a greater loss may be allowed for the same tempera- 
ture rise than with natural cooling. 

With single-phase motors, the efficiency being inherently lower 
than that of continuous motors, the use of forced draught is 
much more necessary to obtain motors of reasonable weight for a 
given output. 

Let us estimate the losses in the motors employed on the Heysham 
line in a similar way to the previous estimations for continuous 
motors. The output of the Siemens motors used on the Heysham 
motor-coaches is 180 hp with forced draught, and the efficiency at 
this output, including gear loss, is seen from Fig. 83 to be 83 per 
cent. 

With this forced draught rating, the input to the motor is — 

=^ X 746 = 161,700 watts, 

and the output from the motor axle to the gear is — 

0-87 X 161,700 = 140,600 watts, 

the efficiency of the motor, excluding gear, being approximately 87 
per cent, at rated load. 

Hence the internal losses amount to 21,100 watts or ( — ' ^ = ) 

7540 watts per ton, since the motor weighs 2 '8 tons. 

This value is considerably above the corresponding figure for 
motors without forced draught ; in fact, a representative value for the 
watts per ton with forced draught may be taken as some 7000 watts, 
as against 4500 watts with natural ventilation. These losses corre- 
spond to a temperature rise of 75° on the 1-hour basis. 

Taking now the Westinghouse motors of the Heysham equip- 
ments, they have an efficiency at rated load of 82 per cent. 



HEATING OF RAILWAY MOTORS 



165 



including gear loss. Thus the input to the motor at the 150 hp 
forced-draught rating is — 

150 X 746 .Qhrnnn ,^. 

— — - — = 137,000 watts. 

[J'oZ 

This motor has a gear loss of 5 per cent, at rated load, therefore the 
output from the motor axle to the gear amounts to — 

0-87 X 137,000 = 119,000 watts. 

This leaves 18,000 watts lost in the motor, and as the motor weighs 
2*5 tons, the loss works out at — 

18,000 ^._^ ,, , 

— ^— - = 7200 watts per ton. 

To compare these figures of 7540 and 7200 watts per ton with the 
corresponding values in continuous motors for the different railways 
dealt with in this chapter, we can bring together the following values 
in Table LVIl.*:— 

Table LVII. — Comparison op Motor Losses for Single-phase and Con- 
tinuous Motors. 



Type of electricity. 


Motor. 


Method of 
Ventilation. 


Cm ^ 

P. 

■^ 


Weight of 
motor 
(tons). 


Average in- 
ternal losses, 
in watts per 
ton at rated 
load. 


Single phase 
>> >> 


Siemens- 

Schuckert 
Westinghouse 


Forced draught 


180 
150 


2-80 
2-50 


7540 
7200 


Continuous electricity 


G.E. 66A 
G.E. 69B 

>> 
Dick-Kerr 


Natural 
>> 
i> 


125 
200 
240 
150 


1-75 
2-51 
2-51 
2-75 


3880 
5390 
7370t 
3640 



These figures must all be taken as merely indicating that on the 
average there is a very considerable difference between the loss per 
ton for natural and forced draught motors. But the precise conditions 
in each case greatly affect the quantitative results and render strict 
comparisons very difi&cult. 



• The subject of the heating of railway motors is also dealt with by Armstrong in 
a paper entitled "A Study of the Heating of Railway Motors," and read before the 
American Institute of Electrical Engineers, vide " Transactions," vol. xix. p. 809. 

t The G.E.69B has openings in the case (see p. 159 and Fig. 84 on p. 161). 



CHAPTER XIII 

TEE WEIGHTS AND COSTS OF ELECTRICAL EQUIPMENTS 
AND OF ELECTRICALLY EQUIPPED TRAINS * 

The weight of an electric passenger train may be divided into four 
parts — 

I. The trucks, including truck frames, wheels and axles, brake 
rigging, etc. ^ 
II. Coach bodies with under-frames, brake cylinders, etc. 

III. Electrical equipment, including motors, rheostats, trans- 

formers, controllers, collectors, compressor motors, cables, 
etc. 

IV. Passengers. 

Although for a given seating capacity, components I. and II. 
increase in weight slowly with increasing schedule speed and decreas- 
ing distance between stops, nevertheless representative weight and 
cost values may be readily assigned to these two items. 

Component III. increases rapidly in weight with increasing 
schedule speeds and with decreasing distance between stops. The 
weight of component III. is also very dependent upon the type of 
electrical equipment. Thus it will be quite different according as 
the continuous, the single-phase or the three-phase system is 
employed. 

The weight of the electrical equipment for a given schedule speed 
and a given number of stops per mile will also be dependent upon 
the continuity of the service. If, after maintaining its schedule for 
a given time, say one hour, a train remains at rest for half an hour 
before again resuming its schedule, these intervals of rest enable the 
electrical apparatus to cool, and consequently the total weight of the 
electrical equipment may be less than for the case of a train required 
to maintain uninterruptedly for, say, 15 hours per day, the same 

* The first portion of this chapter is on the lines of an article contributed by the \ 
author to the Railway Gazette of January 22, 1909. The calculations have, how- 
ever, been completely revised to accord with the more specific and extended data 
since obtained by the author. 

i66 



WEIGHTS AND COSTS 167 

schedule speed with the same number of stops per mile.* In order to 
arrive at a uniform basis of comparison, let us, in this Chapter, con- 
fine our investigation to trains for the latter kind of service, namely, 
trains running uninterruptedly to their schedule for some 15 con- 
secutive hours per day. For such trains it has been found by experi- 
ence that the load on the motors, averaged over the entire run, must 
be of the order of only some 20 per cent, to 25 per cent, of their 
1-hour, 75° C. rated capacity. 

Component IV. of the total train weight is a very variable factor. 
While the number of passengers is often, for a short distance, con- 
siderably in excess of the seating capacity of a train, the average of 
the number of passengers carried by an urban or suburban train 
throughout all its journeys is rarely more than 40 per cent, of the 
seating capacity of the train, and 30 per cent, or, at the most, 35 per 
cent, would be a much more representative figure. 

As will appear later in this chapter, a 180-seat train, equipped 
with continuous electricity apparatus, and designed for operation at a 
schedule speed of 26 ml ph with 1 stop per mile, weighs, without 
passengers, about 88 tons. If one-third of the seats, i.e. 60 seats, are 
occupied by passengers, and if the average weight per passenger is 
62 kg, then the aggregate weight of the passengers is — 

60 X 62 Q.^ ^ 
-1000" = ^ ^ *^'^'- 

This brings the weight of the train up to 917 tons, an increase of 
4 per cent, over the dead weight. Of course, this percentage 
increase varies considerably with the design of the train as regards 
the arrangement of seats, but it will, for a given train, rarely average 
an increase of more than 5 per cent, or 6 per cent. If we take it at 
6 per cent, we shall be within a couple of per cent, of the truth for 
cases when the weight of the passengers for the average conditions of 
load lies between 4 per cent, and 8 per cent, of the weight of the 
train, and this will be the case for practically all trains for city and 
suburban services. 

In the following investigation the total train weight will be taken 
as equal to the dead weight divided by 0'94, i.e. multiplied by 1*06. 
The total train weight is thus made up of the following four 
components : — 



* On London's tube railways a record of 50,000 miles per annum for a single 
train is by no means abnormal. Since the speed is of the order of 16 ml ph, this 
works out at 3100 hours of service per year. But in main-line railways no such 
record is obtained. Thus, on the Heysham branch of the Midland Kailway, although 
the trains run at a speed of some 30 ml ph the annual mileage per train is only 28,500, 
which works out at only 950 hours out of the 8760 hours in the year. 



1 68 ELECTRIC TRAINS 

I. The trucks. 

II. The coach bodies. 

III. The electrical equipment. 

IV. The passengers. 

Let us take the case of a well-built three-coach train, providing 
180 seats, with the usual proportion of first-class and third-class seats. 
Let this train be designed for operation at a schedule speed of 26 
ml ph with one stop per mile. If T is the time, in seconds, of a single 
run from start to stop, and if Q is the duration of each stop in seconds, 
then — 

T + Q = ^ = 138-3 seconds. 

Let Q = 20 seconds. Then — 

• T = 138-3 - 20 = 118-3 seconds. 
The average speed works out at — 

i||| X 26 = 30-4 ml ph. 

From Eig. 46 (page 81), we ascertain that such a train will 
require an electrical equipment providing 11 rated hp on the 1-hour, 
75° C. basis of rating per ton of dead weight of train; but let 
us be conservative, and provide 12 hp per ton of dead weight of 
train. 

The following rough data of weights and costs will serve the pur- 
pose of this investigation : — 

Bogie trucks — 

Weight of each motor-truck, including truck 

frames, wheels, axles, and brake rigging . ^5-5 tons 
Weight of each trailing- truck . . . . =4-0 tons 
Cost of trucks = £22 per ton 

Coach todies — 

Weight of each motor-coach body, complete 

with under-frame, brake cylinders, etc. . . =15 tons 
Weight of each trailer- coach body . . . = 11 tons 
Cost of coach bodies complete . . . . = £80 per ton 

Electrical equipment — 

Weight of continuous-electricity equipment = 19 kg per rated hp 
„ of single-phase equipment . . = 40 kg per rated hp 
Cost of electrical equipment . . . = £125 per ton 
Let us work out the weight of, — tirst, a continuous-electricity train, 

and, secondly, a single-phase train. 



WEIGHTS AND COSTS 169 

I. Train with Continuous-Electricity Equipment. 

I shall make the preliminary assumption that a suitable train for 
the required capacity and schedule will comprise two motor-coaches 
and a trailer interposed between them, and that only one of the bogies 
on each motor-coach will require to carry motors. 
Thus we have — 

2 motor-bogies at 5*5 tons . . . . . = 11 tons 
4 trailing-bogies at 4*0 tons . . . . = 16 „ 

2 motor- coach bodies at 15 tons . . . . = 30 „ 
1 trailer-coach body at 11 tons . . . . = 11 „ 

Weight, exclusive of electrical equipment . . =68 tons 

Let us denote by W the weight of the electrical equipment in 
tons. An outside figure for modern railway equipments employing 
continuous motors, each of from 150 to 250-hp rated capacity, is 19 
kg per rated hp, and since we require 12 rated hp per ton of dead 
weight of train (= 68 4- W) we have — 

W = 0*019 X 12 X (68 -1- W) = 20 tons 
.". Dead weight of train =68-1-20 = 88 tons 

Consequently — 

the rated capacity of electrical equipment = 88 X 12 = 1056 hp 
This may be provided by four 265-hp motors and the auxiliary 
apparatus. 

We may estimate the cost as follows : — £ 

Trucks (= 22 X 27) =590 

Coach bodies (= 80 X 41) = 3280 

Electrical equipment (= 125 x 20) . . . = 2500 
Labour in assembling (= £6 per ton) . . . = 530 

Total cost of train = 6900 



„ „ per ton = £78*5 
„ „ per seat = £38*3 

II. Train with Single-phase Equipment. 

We shall require to provide 8 motors — one for each axle. Thus 
we have — 

4 motor-bogies at 5 "5 tons =22 tons 

2 trailer- bogies at 4*0 tons . 
2 motor-coach bodies at 15 tons 
1 trailer-coach body at 11 tons 

Weight of train, exclusive of electrical equipment 



;:; 


8 


J\JJLXU 


= 


30 


)) 


•= 


11 


>> 


~~ 


71 tons 



170 ELECTRIC TRAINS 

We may again denote the weight of the electrical equipment 
by W. Now, single-phase electrical equipment, when the component 
motors are of 150 to 250 -hp rated capacity, have a weight of 40 kg 
per rated hp. We again require 12 rated hp per ton of dead weight 
of train ( = 71 4- W). We now have — 

W = 0-040 X 12 X (71 + W) = 66 tons 
/. Dead weight of train = 71 + 66 = 137 tons 

Consequently — 

the rated capacity of electrical equipment = 137x12 = 1644 hp 

This may be provided by eight 210-hp motors and auxiliary 
apparatus. 

The cost works out as follows : — £ 

Trucks (= 22 X 30) = 660 

Coach bodies (= 80 X 41) = 3280 

Electricalequipment (= 125 X 66) . . . = 8250 

Labour in assembling (= £4 per ton) . . = 550 



Total cost of train = 12,740 



„ „ per ton = £93 
„ „ per seat = £70*8 

Thus for our two 180-seat trains operating a 26 ml ph 1-stop-per- 
mile service we have the results given in Table LXYIII. 

Table LVIII. — Particulaes of 180-seat Teains with Continuous and Single- 
phase Equipments. 

Continuous. Single-phase. 

Dead weight of train in tons 88 . 137 

Total cost of train £6900 . £12,740 

Ditto per ton £78*5 . £93 

Ditto per seat £38-3 . £70-8 

Dead weight of train in tons per seat .... 0'481 . 0*761 

In order to arrive at a rough estimate of the relative annual costs 
for capital, depreciation, maintenance and renewals, let us assign 15 
per cent, of the cost to cover these factors. These annual costs are 
thus respectively — 

Per train £1035 . £1910 

Per ton £11-8 . £U'0 

Per seat £5-8 . £10-6 

Let US next endeavour to estimate a reasonable figure for the 
number of miles which should be travelled by each train per year. 
Allowing each train to be in service for 160 days in the year, and 



WEIGHTS AND COSTS 171 

keeping it in operation to its schedule for 15 hours out of each day 
that it is in service, we find that each train is in service for — 

160 X 15 = 2400 hours per annum. 

During this time, at 26 ml ph, such a train will cover — 

26 X 2400 = 62,400 miles. 

In Fig. 45 (page 80) we see that for this 26 ml ph one-mile 
schedule, a conservative value for the input to the train from the 
third rail or overhead conductor will be some 110 w hr per ton-mile. 

This figure, however, relates to test runs. In practice, allowing 
for all the exigencies of everyday service, such as shunting, lighting, 
making up time of delayed trains, and the various other contingencies 
of routine service, the consumption may be taken as averaging, per 
ton-mile of recorded service, a 20 per cent, higher amount, bringing 
the gross input to 132 w hr per ton-mile. Taking into account that 
the total train weights, including passengers, are — 

For continuous electricity . . . 1 '06 X 88 = 93 tons 
„ single-phase 1*06 X 137 == 145 „ 

and that the corresponding gross inputs are — 

w hr per kw hr per 
ton-mile train-mile 

Gross input for continuous electricity train . 132 12*3 
„ „ „ „ „ . loZ ly"l 

Let us take the over-all efficiency from the generating station to 
the train as 80 per cent, for the continuous-electricity system, and 90 
per cent, for the single-phase system. Then the outputs from the 
generating station are as follows : — 

For the continuous-electricity 1 12*3 ^ ^ . , , , . .. 

system . . . . | = 0^ = ^^'^ ^^ ^^ P^' train-mile 

19'1 
For the single-phase system = ^^7^^ = 21*2 „ „ 

Since each train covers 62,400 miles per annum, the outputs per 
train per annum are as follows ; — 

Continuous electricity 62,400 X 15 4 x 10"® = 0*96 million kw hr 
Single phase . . 62,400 x 21'2 x 10"^ = 1-32 

For a service of this sort, provided there are sufficient trains always 
in service to ensure some approach to a uniform load, electricity could 
be purchased from supply companies in many districts at 0'50^. per 
kw hr of high pressure, three-phase electricity as delivered from the 
generating station, and at 0'55d, if supplied from the generating 
station as high pressure, single-phase electricity. This would not 
include any costs pertaining to the transmission line from the 



172 ELECTRIC TRAINS 

generating station to the railway. The cost of electricity per train 
per annum would thus be — 

Continuous electricity . . . — ^j^r = £2000 

Q. 1 . 1,320,000 X 0-55 p^^^^ 

Smgle-phase — —tvtk = £3020 

^ ^ 240 

The interest, depreciation, and maintenance for a train, and the 
cost of the electricity for the train, are only two of many large items 
associated with the total cost of running the train. AH the other 
items may, however, be taken as coming, in the aggregate, to sub- 
stantially the same total, independently whether the continuous- 
electricity system or the single-phase system is employed. Thus with 
the heavy single-phase trains the maintenance and depreciation of 
the permanent way will be much greater than with the relatively 
light continuous-electricity trains. The cost of single-phase overhead 
construction is greater than that of third-rail construction. These 
two items will fully offset the greater cost of the sub-station 
machinery in the continuous-electricity system. It is here only 
proposed to compare the components which we have estimated, as 
these are the ones including the most essential disparity. 

Thus we arrive at values set forth in Table LIX. — 



Table LIX. — Annual Costs for 180-seat Trains with Continuous and Single- 
phase Equipments. 

Continuous c!.,„i„ »t,»o.> 
electricity. Single-phase. 

Dead weight of train 88 tons . 137 tons. 

A — interest, depreciation, and maintenance of one 180- 
seat, 26 ml ph, 1 stop-per-mile train, per annum . . £1,035 . £1,910 
B — outlay for electricity for one train per annum . . £2,000 , £3,020 

(A + B) £3,035 . £4,930 

Mileage per train per annum 62,400 . 62,400 

(A + B) per train-mile ll'ld. . 19'0d. 

„ „ ton-mile 0'133d. . 0'139(£. 

„ „ seat-mile 0-0656Z. . 0-105d. 

Thus the single-phase system costs at least some (19'0 — 11*7 
= 7'3) more per train-mile for this particular capacity of train, and 
for this particular schedule, than the continuous-electricity system 
costs. 

There are, of course, many other expenses associated with train 
operation, and the total costs of all kinds would usually aggregate, 
for a 180-seat train, at least some S5d. per train-mile, or a matter of 
from two to three times the above value of (A + B). But since, as 
already pointed out, A and B are the components chiefly affected by 
the choice between continuous-electricity and single-phase operation, 
then, whatever be the precise value of the total costs, the difference 



WEIGHTS AND COSTS 



173 



against single -phase will, for a train of this capacity and for this 
schedule, be a matter of some Id. per train-mile. Thus, if the total 
cost per train-mile is, for continuous electricity, of the value set forth 
in the first column of Table LX., then the single-phase cost per 
train-mile will be of the value set forth in the second column, and the 
percentage by which the latter exceeds the former cost will he, of the 
value shown in the third column. 



Table LX. — 180-seat Train, operating to a Schedule op 26 ml ph, with One 
20-sECOND Stop Per Mile, and aggregating 62,400 miles Service run Per 

Year. 



Cost per train-mile. 


Percentage greater cost of 


Continuous electricity. 


Single phase. 


the single-phase train. 


35d. 
40d. 
45d. 
50^. 


42d. 
47d. 
52d. 
bid. 


20 
17 
15 
14 



The average fare for urban and suburban railways, taking into 
account all classes, as also workmen's fares, is around 0'6c?. per mile. 
But since a seat is, on the average, occupied for — say, 33 per cent, of 
its journey — the receipts per seat mile are around — 

0-33 X 0-60 = {)-2M, 

The receipts per train-mile are thus of the order of — 

180 X 0-20 = 36^. 

Thus it is evident that the difterence between the costs of the two 
systems is more than sufficient to provide for, or wipe out dividends, 
were electrification introduced on an extensive scale. Or, looking at 
the matter from the opposite standpoint, if, as its advocates claim, 
single-phase can, under these conditions, compete with steam, then 
the use of the continuous-electricity system would render available 
for dividends, or for reserve funds, or for expenditure in improving the 
railway, a further large percentage of the gross receipts. 

On the whole, my figure of 0'6c?. per mile for the average fare 
errs on the side of being rather high. I have taken it with a view to 
giving the single-phase system the benefit of any doubt on this score. 
It is evident from the table that the lower the gross receipts per 
train-mile, the more unfavourable to the single-phase system are the 
results of the comparison. For the last six months of the year 1909, 
the receipts from passengers on the Baker Street and Waterloo 
Eailway, the Great Northern Piccadilly and Brompton Eailway, and 



174 ELECTRIC TRAINS 

the Charing Cross, Euston and Hampstead Kail way, averaged 0*1896?. 
per seat-mile. 

It will be pointed out that the case I have taken, namely, a 
service in which, with one stop per mile, a schedule speed of 26 miles 
per hour is maintained, is rather a severe service. I am quite aware 
of this. But it is the very ability to provide such a service which is 
often a chief inducement to introduce electric operation. If, still with 
one stop per mile, we come down to a schedule speed of, say 20, ml 
ph, while electrification is highly desirable, there are not (except for 
mountain roads and for tunnels and elevated roads) so strong 
advantages in its favour as exist in the case I have taken for my 
example. While at the lower speed (with one stop per mile) the 
disparity between single-phase and continuous electricity is dis- 
tinctly diminished, the advantage for continuous electricity is still 
too great to be overlooked. At the slow schedule of 16 ml ph and 
one stop per mile, or with any schedule equivalent to this, such 
as still lower speeds with more frequent stops, or higher speeds 
and less frequent stops (as on the Midland Railway electrification 
at Heysham), we come to the range of work where, so far as relates 
to the rolling stock, it is of much less consequence which system is 
employed. But for so unattractive a service, there will rarely, with 
present developments, be found sufficient economic advantage to 
justify substituting electricity for steam. 

A point which has not been sufficiently appreciated is the large 
percentage which the rolling stock constitutes of the total capital 
outlay of urban and suburban railways. 

Thus take the case of 50 miles of double track, over which trains, 
each with a seating capacity for 450 passengers, are operated at a 
headway of 2 J minutes and at a speed of 16 ml ph with 2 stops per 
mile. For such a service the trains may be taken as accomplishing 
an aggregate of some 14 million train miles per annum. The dis- 
tribution of the electrification and rolling stock costs is somewhat as 
follows — £ 

Generation Station 800,000 

Transmission system, including sub-stations . 1,600,000 
Continuous-electricity rolling stock . . 3,200,000 

Total . . . . 5,600,000 



I 



The rolling stock constitutes 57 per cent, of the total, and the 
maintenance and depreciation thereon are enough greater than on the 
other items, to raise the annual costs associated with the third item 
to some 75 per cent, of the annual costs associated with the total of 
the three items. 

It is thus evident that a serious disadvantage of the single-phase. 



WEIGHTS AND COSTS 



175 



as compared with the continuous-electricity system, is the relatively 
greater weight and cost of the rolling stock. This disadvantage 
becomes less the greater the distance between stops and the lower 
the schedule speed. In other words, we may say that, in respect to 
seating capacity, the single-phase system is, as regards weight, at a 
less disadvantage the less the severity of the schedule. 

In Fig. 85 are given the results of carefully prepared estimates of 

/,0 



% 



^ 



































/ 


















/ 


/ 
















y 


/ 




y 


/ 






A 




x^ 


/^ 




^ 


/ 






^^ 


A, 








"^ 













' 






^ 















































































/0 20 2^ "^ 32 

5chec/u/e Speed -m/fih 

Fig. 85. — Curves showing Weights of a 180-Seat Train for Various Schedule Speeds 

with One Stop per Mile. 
Curve A, for Single-phase Equipment. 
,, B, „ Continuous Equipment. 

the weights of rolling stock per seat for 180-seat trains designed 
for operation at various schedule speeds with one stop per mile, and 
equipped respectively with continuous and single-phase apparatus. 
We see from the figure that for so light a schedule as 15 ml ph and 
one stop per mile there is, so far as relates to the weight of the 
rolling stock, no difference worth considering between continuous 
and single-phase trains. But already, at 24 ml ph, the single- phase 
train weighs 35 per cent, more than the continuous-electricity train, 



176 



ELECTRIC TRAINS 



and at 28 ml ph the excess is 60 per cent. For a total train weight of 
0'5 ton per seat the continuous train is suitable, with one stop per mile, 
for a schedule speed of 26 ml ph, as against a schedule speed of only 
20 ml ph for the single- phase train. 

Corresponding curves of the cost are given in Fig. 86. From 
these curves we see that for low speeds the cost of the train per 
seat is of the order of £30 to £35, and that the difference between 



/OCX 



sa 
I- 























































1 


















/ 


















/ 


/ 






y 






A 




X 


^ 




^^ 


y 


r^ 




- 


M^ 








^ 


^*^^ 










B 



























































/0 20 e^ ^e SZ 

Fig. 86. — Curves showing Costs of a 180-Seat Train for Various Schedule Speeds 

with One Stop per Mile. 
Curve A, for Single-phase Equipment. 
,, B, „ Continuous Equipment. 



the two systems, so far as relates to this feature, is slight. With 
increasiug schedule speeds, however, the difference in cost rapidly 
increases. At some 22 to 23 ml ph (with one stop per mile) the 
single-phase train costs 50 per cent, more than the continuous- 
electricity train, and at 27 ml ph the cost of the single- phase train 
is twice that of the continuous- electricity train. The difference in 
cost is strikingly brought out in the following table : — 



WEIGHTS AND COSTS 



177 



Cost of train 


Appropriate schedule speed in ml ph 
with one stop per mile. 


per seat. 


Continuous-elec- 
tricity train. 


Single-phase 
train. 


£40 
£50 


27 
30 


19 
23 



These results show that for the railway electrification work at 
present confronting engineers, i.e. for the range of work where 
electrical methods are distinctly preferable to steam-locomotive 
methods, the system employing series- wound, continuous-electricity 
motors is decidedly the most appropriate. 

Extensive areas may be served by the system of traction employing 
continuous-electricity motors on the trains by the plan, now almost 
invariably used,of employing large,high-pressure,alternating-electricity 
generators to provide the electricity in the first instance. The pressure 
employed at these alternating-electricity generators is usually of the 
order of from 10,000 to 12,000 volts. The use of these high 
pressures, enables the Electricity Supply Station to be located at some 
site selected with reference to economical considerations, and often 
at a very considerable distance from the trains where the energy is 
required. Thus a site at the side of a river or canal may, from 
considerations of the cheapness of land, the facilities for bringing 
coal, and the plenitude of circulating water, permit of providing 
electricity at a much lower price than would be possible were the 
location of the Electricity Supply Station determined solely with 
reference to its proximity to the location where the electricity is 
required, namely, at the trains. The very nature of the requirements 
of railways involves the necessity of supplying electricity over 
extensive areas, and it is also essential to the economical application 
of electricity to power supply purposes that there shall be some 
approach to a uniform load on the station. Many trains must be 
simultaneously operated from the same Electricity Supply Station in 
order that their fluctuating individual requirements shall overlap to 
such an extent as to provide an aggregate load of suiB&cient uniformity 
to consist with commercial economy. Thus it has become recog- 
nized as fundamental that a large area shall be served from a single 
Electricity Supply Station. The Lots Eoad Electricity Supply Station 
at Chelsea, for example, at the times of maximum load, supplies 
electricity simultaneously to some 165 trains scattered over an area 
some 25 miles long and some 10 miles wide. Of course, when a 
certain distance has been reached, the cost of the copper transmission 
line becomes sufficiently great to justify a second Electricity Supply 

N 



178 ELECTRIC TRAINS 

Station from which the trains shall draw the energy necessary for 
their propulsion when they have passed over from the area supplied 
by the first station. Usually, however, a single Electricity Supply 
Station has sufi&ced, even for very extensive undertakings. Thus the 
Lots Eoad Station supplies on the aggregate, some 60 miles of double 
track and involves, during the times of heaviest traffic, between 
200 and 300 trains in service, each train requiring an average output 
from the generating station of some 100 kw. 

It is practicable for two independent railways serving adjacent 
or overlapping areas, and enjoying running powers over one another's 
lines, to each have its own Electricity Supply Station and to interlink 
their circuits. In such cases, each railway provides substantially 
that portion of the total electricity which it requires for its own 
sections, but there is usually no hard-and-fast demarcatioo. As 
an instance of this plan may be cited the fact that the Lots Eoad 
Electricity Supply Station of the London Underground Railways Co., 
and the GJ miles distant Neasden Eectricity Supply Station of the 
Metropolitan Railway are thus interlinked. The total length of the 
line served by the two interlinked systems is some 80 miles of double 
track. Several other equally extensive systems served by only one 
or two Electricity Supply Stations are in operation in various parts of 
the world, and their number is rapidly increasing. Consequently, it 
may be claimed to have been definitely established that the system 
of railway electrification employing high-pressure three-phase alter- 
nators at the Electricity Supply Station, and carrying 600-volt, series- 
wound, continuous-electricity motors on the trains for the purpose of 
their propulsion, is thoroughly appropriate for serving enormous 
areas in all instances where the density of the traffic is great 
throughout the area. A fairly dense traffic is essential, since other- 
wise the overlapping of the demands of the individual trains will not 
be sufficient to ensure that the apparatus at the Electricity Supply 
Station is constantly carrying so considerable a percentage of the 
load for which the station is designed, as to permit of supplying 
the electricity at a low cost. Thus, it would be absurd to have an 
Electricity Supply Station whose load consists of only one train 
equipped with electric motors fed from this station. If the maxi- 
mum load required by the train should be 1000 hp, then the maximum 
capacity of the station would also be 1000 hp. But a station to serve 
100 such trains would require to have a capacity, not of 100 X 1000 
= 100,000 hp, but only, say, some 10 X 1000 = 10,000 hp, since 
the 100 trains would not make their maximum demands at the same 
time. Thus 100,000 hp aggregate capacity of steam locomotives 
would be replaced by only 10,000 hp aggregate capacity of steam 
engines in the Electricity Supply Station. And whereas the annual 
efficiency of each of the 100 small 1000-hp non- condensing locomotives 



WEIGHTS AND COSTS 179 

would only be at the most 3 per cent., the combined annual efficiency 
of the boiler plant and the four 2500-hp condensing turbines which, 
in such a case, would be installed in the Electricity Supply Station 
would be of the order of 12 per cent., and the annual over-all efficiency 
of the station, from the coal pile to the outgoing cables, would be of 
the order of 10 per cent. In cases where electrical operation is a 
sound proposition, the annual outlay for coal at the Electricity Supply 
Station is far less than would be the outlay for the coal which would 
be burned in the locomotives which would be required to maintain 
the same service of trains.* The cost of the electrical equipment 
brings up the total cost of rolling stock to the rather high figure of 
some £80 per ton of total weight of train, and it should not be claimed 
that electrical methods have any advantage as regards the decreased 
initial cost of a train of a given seating capacity. In fact, the con- 
trary is the case, but owing to the much greater schedule speeds 
rendered practicable by electrical methods, the annual capital cost of 
the rolling stock per train-mile is brought to a much lower figure 
than is attained on urban and suburban routes by steam-locomotive 
trains. A very great advantage also accrues from the fact that, with 
given terminal facilities, twice as many electrical trains can, as 
pointed out by Mr. Aspinall,t be dispatched within a given time 
than is the case with steam trains. 

When we come to a consideration of the permanent way, it is now 
usually agreed that the rails are subject to a decidedly more rapid 
deterioration on electric than on steam 'roads. This circumstance, 
together with the large outlay for the third rail, or overhead con- 
struction, brings the annual outlays which must be allocated to 
structures and apparatus throughout the length of the permanent way, 
much higher per mile with electricity than with steam locomotives. 
But in view of the high speed and dense traffic rendered practicable 
with electrical methods, here again the outlays per train-mile are 
less than with steam-locomotive services. 



* On p. 606 of the " Proceedings of the American Institute of Electrical Engineers " 
for April, 1910, Mr. W. S. Murray states that some tests have been made with 
20 steam-locomotives on the New York, New Haven and Hartford Railway, to 
compare the coal consumption with that for electric trains rimning under the same 
conditions. He states that for the density of trafiBic on that road, they have found 
that the coal burned at the Electricity Supply Station is only one half as great as 
that burned with an equivalent steam-locomotive service. 

t Mr. Aspinall puts the case as follows : " Every time a locomotive train comes 
in and goes out, you have four platform operations and eight signal operations. 
First of all, the train comes in, then a locomotive follows it, that is two ; then the 
train goes out, that is four platform operations, which means eight signal operations. 
The electric motor train comes in, that is one ; the motor-man goes to the other end 
of the train, and the train goes out, that is two. You have only two platform 
operations and four signal operations. The result is that, by using motor-car trains 
instead of locomotives, you double the capacity of your terminal accommodation." 



i8o ELECTRIC TRAINS 

Thus, the fundamental condition for obtaining an adequate return 
for the heavy costs entailed in "electrifying" a section of steam 
railway, is that the electric service shall provide very frequent 
trains. During the hours of densest traffic, some of the London 
tube railways provide a service, in each direction, of forty trains per 
hour. This corresponds to one train every 90 seconds. This is in 
striking contrast to the conditions on extensive sections of main-line 
railway situated at considerable distances from cities. On such 
sections, only some couple of trains would pass a given point 
in one direction in the course of an hour. Obviously, under such 
circumstances, the proposition to obtain the power from a distant 
generating station loses force, since the cost of the structures for 
conveying the electricity to the train works out at a high value 
per train-mile, and the advantages of the self-contained steam- 
locomotive are very evident. 

If, under these conditions, some autocrat were, nevertheless, to 
require the supercession of the steam-locomotive by the electric 
motor, the single-phase system would legitimately come into con- 
sideration. From the point of view of the single-phase system, 
the irony of the situation arises from the circumstance that in the 
field where its economy is more or less on a par with that of the 
continuous-electricity system, the steam-locomotive can usually more 
than hold its own in comparison with electrical methods. 



CHAPTER XIV 

SUMMARY AND CONCLUSIONS 

In a lecture which I delivered in October, 1909, at the School of 
Military Engineering at Chatham,* I pointed out that in the earlier 
instances of the application of electric motors to the propulsion of 
railway trains, the chief motive was usually quite dissociated from 
any question of the superiority of the electric motor over the steam 
locomotive as regards capacity or economy. In many instances, the 
complete elimination of smoke from tunnels was practically the 
exclusive reason for the adoption of electricity. This same feature 
of the absence of smoke in tunnels and railway stations, and even 
on overhead railways, continues to play no small part in the favourable 
reception which has been accorded to electrically-propelled trains. 
Owing to difficulties with steam and smoke, the steam locomotive 
would be altogether inadmissible for hauling trains in the deep-level 
tubes which now play so important a part in the transportation 
arrangements of London. Had it not been for this feature of 
cleanliness a much longer time would have been required to attract 
to the proposition of railway electrification the very serious attention 
which it now commands. Amongst the installations where electricity 
has been adopted primarily to eliminate smoke difficulties may be* 
mentioned the New York Central Eailway, the Pennsylvania Eail- 
way, and the New York, New Haven and Hartford Eailway, which 
all enter New York through long tunnels, the Baltimore and Ohio 
Eailway, the Simplon Tunnel Eailway, the Cascade Tunnel of the 
Great Northern Eailroad, U.S.A., the Mersey Eailway, the tube 
railways of London, the Metropolitan District Railway and the 
Metropolitan Eailway in London, the Berlin Overhead and Under- 
ground Eailway, the St. Clair Tunnel of the Grand Trunk 
Eailway System, and the Metropolitan Underground Eailway of 
Paris. Unfortunately, on British Eailways the restricted dimensions 
of the tunnels often render them a hindrance rather than an incentive 
to the introduction of electrical methods. In this respect the conductor 

* In this chapter I have made use of certain portions of my Chatham lecture. 

i3i 



l82 



ELECTRIC TRAINS 



rail is more amenable to the ruling conditions than is the overhead 
conductor system. 

It has, however, been for some time clearly recognized that the 
electrical methods which have already come into fairly extensive use 
on railways possess inherent attributes which in themselves suffice, 
quite aside from the first-recognized important feature of greater 
cleanliness, to ensure their ultimate general adoption for a very wide 
field of railway work now usually done by means of steam locomotives. 




20 30 ^w 

Schedule Speed in ml ph 



7^ 



Fig. 87. — Curves showing the Acceleration in ml phps necessary to maintain Various 

Schedule Speeds for several Distances between Stops, 
m = S.L.E. Ely. — Schedule Speed 22 ml 'ph. Acceleration 1*0 ml phps. Average 

Distance between Stops 0*88 Mile. 
% = L. &Y. Ely. — Schedule Speed 30 ml ph. Acceleration 1*0 ml phps. Average 
Distance between Stops 1-32 Mile. 



i 



provided that no adequately radical improvement in the steam engine 
is brought forward. 

In Fig. 87 is shown, for runs of lengths varying from one-half 
mile up to eight miles between successive stopping-places, the inter- 
dependence which exists between the accelerations and the attain- 
able schedule speeds. In the preparation of .these curves I have 
taken the deceleration during braking as some 1'5 ml phps, and the 
duration of the stops at stations as 20 seconds. I have taken 
reasonable characteristics for the speed-time diagrams by means of 
which the data plotted in Fig. 87 have been derived. From these 
curves it will be seen that while with one stop per mile, an acceleration 
of 0*4 ml phps only permits of obtaining a schedule speed of some 



SUMMARY AND CONCLUSIONS 183 

17 ml !ph we can, by doubling this acceleration, i.e. by employing 
an acceleration of 0*8 ml phps obtain a schedule speed of some 
23 ml ph, that is to say, we can increase the schedule speed by 35 
per cent, Now, for suburban traffic, the practicability of obtaining 
high schedule speeds, at the same time providing stops every mile, 
or even every half-mile, is of enormous commercial importance. With 
present steam-locomotive practice, where suburban passenger trains 
are rarely accelerated at more than 0*4 ml phps, the attainment of 
a schedule speed of 22 ml ph is only practicable when the stopping- 
places are at least 1*7 mile apart. But with electrically-equipped 
trains, an average acceleration of 1 ml phps is in accordance with 
thoroughly established practice, and this ratio permits of operating 
to a schedule speed of 22 ml ph even when the stops are only 
0*8 of a mile apart. Thus, the use of electrically-operated trains for 
a suburban service permits of having, on a given route, twice as many 
stops as with trains hauled by steam locomotives, and of nevertheless 
maintaining the same schedule speed. 

Conversely, we may, for the two methods of propulsion, compare 
the schedule speeds corresponding to a given distance between stops. 
This leads us to the result that, with a stop every 0*8 mile, the schedule 
speed with electric trains will be 22 ml ph as against a schedule 
speed of only some 14 ml ph for trains hauled by steam locomotives. 
The relation shown in the curves in Fig. 87 as existing between 
the accelerating rate and the attainable schedule speed is based on the 
inevitable relations between space and time. The allocation of the 
high acceleration to electric trains, and of the low acceleration to trains 
hauled by steam locomotives, is based on experience. As instances 
of electric railway practice in this country, I may cite the Liverpool - 
Southport electrified section of the Lancashire and Yorkshire Eail- 
way, where trains equipped with series-wound, continuous-electricity 
motors are regularly operating to the schedule indicated at point 
n in Fig. 87. This point corresponds to a schedule speed of 30 
ml ph over a route with 1 stop every 1*32 mile. Point m corre- 
sponds to the schedule for the single-phase electric trains in operation 
on the 9-mile section of the L.B. & S.C. Kailway between London 
Bridge and Victoria, and known as the South London Elevated Eail- 
way. The average distance between stops on this railway amounts 
to 0'88 mile and the schedule speed is 22 ml ph. Still higher accele- 
rations have been employed on electric railways and might be cited, 
but, on the whole, the economical range appears to be of the order of 
from 1*0 to 1-5 ml phps for high- speed electric trains making frequent 
stops.* 

It is true that steam locomotives may be designed which will be 

* See p. 5, Chapter I. 



1 84 ELECTRIC TRAINS 

capable of accelerating trains at a much higher rate than 0*4 ml 
phps. But just as the economical limit for electrically-equipped 
trains appears now to have been established by experience to be of 
the order of from 1*0 to 1*3 ml phps, although twice this rate 
could readily be provided were it justifiable to go to the necessary 
expenditure, and were the greater total train weight immaterial; 
so, also, it appears now to have been established by experience 
that the economical limit for trains hauled by steam locomotives 
is, for such a service, of the order of 0*4 ml phps, although 
there is no reason why twice this rate, or even more, could not 
be provided were questions of cost and weight not of consequence. 
Obviously, the acceleration corresponding to a given tractive effort 
exerted by a locomotive is dependent upon the weight of the train 
behind the engine. If, with a given weight of train, a certain engine 
accelerates at 0*3 ml phps it will, with a train of only half this weight, 
accelerate at 0"6 ml phps. 

Let us consider a train operated by continuous electricity, employed 
on the Liverpool and Southport section of the Lancashire and York- 
shire Eailway. It has already been stated that the point n of Fig. 
87 relates to this train. The train comprises 4 coaches, and its 
complete weight is 144 tons. The train is made up of 2 motor- 
coaches, on each of which all four axles are driven, and of 2 inter- 
mediate coaches not carrying any propulsion equipment. Thus, out 
of the train's 16 axles, 8 are driven by motors, and these 8 axles carry 
92 tons out of the 144 tons total weight of the train. Owing to the 
uniform turning effort of electric motors, slipping rarely takes place 
with electric trains until the tractive effort of the motor amounts to 
some 25 to 30 per cent, of the weight on the driven axles. Indeed, 
instances are on record where, when sand has been used, the coefficient 
of adhesion has amounted to 0*35. Thus, it will be agreed that it is 
conservative to take the adhesion in the case of electric trains, at 25 per 
cent. On the basis of 25 per cent, adhesion, we arrive at the result 
that the wheels will not slip until the 8 motors are exerting a tractive 
effort of 23 tons. This tractive effort, which would, on a level track, 
correspond to the high acceleration of 3 ml phps, would call for a 
current much in excess of that for which the motors and apparatus 
have been designed, and the calculation has been given simply to 
illustrate the point that, with electrical traction methods, considerations 
of adhesion far less often impose limitations than is the case with 
steam-locomotive methods. 

The steam train must carry not only its own motor, the steam 
engine, but also its steam-raising apparatus and its fuel, and the com- 
bined plant cannot, for a given capacity, be reduced to any such small 
volume and low weight as has become standard for electrical equip- 
ments. In electric traction, with specially severe conditions, it is only 



SUMMARY AND CONCLUSIONS 185 

the increased weight of the motor and its controlling apparatus which 
affects the total train weight ; the severe conditions as regards the 
steam-raising apparatus and the weight of the fuel are transferred to 
the electricity generating station, whereas with trains hauled by steam 
locomotives any increase in the severity of the service entails 
increased size and weight, not only of the engine, but of the steam- 
raising apparatus which is carried on the train. Thus, the weight of 
trains hauled by steam locomotives more greatly exceeds the weight of 
electric trains for the corresponding service the greater the severity 
of the service. The severity of the service is, for good level tracks, 
chiefly proportioned to the frequency of the stops and the schedule 
speed. Thus, it is especially in the case of suburban services 
that electrical methods are superior to steam-locomotive methods as 
regards the advantages of lesser total train weight. In the earlier 
chapters of this treatise I have shown that it is exactly for these 
severe services, namely, for high speeds and frequent stops, that a 
low train weight per passenger carried, or per seat provided, is of great 
commercial importance. I have shown this to be a consequence of 
the most characteristic feature of the mechanical problem of operating 
trains at high schedule speed notwithstanding frequent stops. This 
characteristic feature relates to the circumstance that, of the total 
energy required by the train, a preponderating percentage is used 
in providing the momentum of the train at its crest speed, and that 
nearly all this energy of momentum is subsequently wasted as heat 
at the brake-shoes. I have shown in Chapter III. (see Fig. 21, p. 40), 
that in the case of a schedule speed of 18 mlph, with stops every half- 
mile, the energy stored up in the train as momentum at the instant when 
the crest speed is attained, amounts to some 55 per cent, of the total 
energy consumed by the train during the run. With 4 miles between 
stops, however, even at a schedule speed of 30 ml ph, the percentage 
stored up as momentum at the instant of crest speed is only some 
30 per cent, of the total energy consumed by the train during the run. 
Eor a half-mile run at a schedule speed of 18 ml ph only some 22 
per cent, of the energy consumed by the train is usefully expended in 
its propulsion. But for a 4-mile run, even at 30 ml ph, some 55 per 
cent, of the total energy consumed by the train is usefully expended 
in its propulsion. For a service with frequent stops, so small a part 
of the total energy consumed is available for propulsion, that the 
total input to the train per ton of weight is inevitably very high, and 
it becomes of the utmost importance to keep down the cost of the 
energy consumed by the train by keeping down the weight of the 
train. This state of affairs should be contrasted with the conditions 
of long-distance, non-stop runs. For such conditions, where steam- 
locomotive methods are most appropriate, weight is of decidedly less 
consequence, since the energy stored up as momentum constitutes an 



1 86 ELECTRIC TRAINS 

utterly negligible part of the total energy consumed by the train in 
making its journey. In such a case, by far the greater part of the 
energy required by the train is consumed in overcoming the friction 
of the track and bearings, and the air friction at the ends and sides 
of the train. But little is gained in such service in reducing the 
weight of the train. 

But in suburban, high-speed, frequent-stop services, the energy 
required is closely proportional to tide weight of the train, since 
it is largely represented by the momentum of the train at its crest 
speed. Herein, therefore, we see at once, the chief reason why 
electrical methods are so much more suitable for high-speed, 
frequent-stop services than steam-locomotive methods can be. 

The transit facilities of London, New York, Berlin, Paris and, in 
fact, of all the large capitals of the most progressive countries, as well 
as of the immediate suburbs of these capitals, have now, for some 
years, comprised magnificent systems of electrically-operated railways. 
To these instances there are now gradually being added the sections 
of main-line railways radiating out some twenty miles or more from 
their city termini. This latter movement is proceeding very gradually. 
It is retarded by the circumstance of the inherent inappropriateness 
of electrical methods where the traffic is sparse. Thus, while for some 
20 to 25 miles out from London the service of all main-line railways 
is either already dense, or would rapidly become so under the conditions 
attending electrification ; it would be essential, in the interests of 
economy heyond this 25-mile zone, to change over from electric to 
steam-locomotive propulsion. The necessity of admitting the 
superiority of steam-locomotive methods for long-distance, non-stop 
runs inclines the railway managements to postpone taking up the 
question, the more especially since there is the further difficulty of 
justifying in advance, the large capital expenditure incurred in electri- 
fying the termini and the area contained within the 25-mile radius. 
The suburban traffic of a main-line railway is a very large component 
of its total business. While the length of route is but a small pro- 
portion of the railway's entire length of route, this relatively small 
length is so intensely utilised that the train-mileage within the 
suburban zone must constitute a large percentage of the total train- 
mileage of most of the railways entering London, and it would not be 
commercially justified to subordinate the interests of this large traffic 
by inflicting upon it some less appropriate electrical system on the 
plea that that system is the most appropriate for main-line work. 
More especially is this the case in view of the fact that the steam 
locomotive is well adapted to handle all except the suburban sections 
of a main-line railway. 

Largely owing to the importance of employing trains of light 
weight, it is now generally agreed that of the various leading systems 



SUMMARY AND CONCLUSIONS 187 

of electrical propulsion, the system employed on the train, series- 
wound, continuous-electricity motors is distinctly the best for 
suburban services with high speeds and frequent stops. The 
three leading systems of electric railways employ on the trains 
respectively — 

I. Three-phase motors. 

II. Continuous motors. 

III. Single-phase motors. 

The three-phase motor is preferable to either of the other two types so 
far as relates to its light weight. For the service in question, however, 
i.e. for the particular sort of service where steam-locomotive methods 
are at the greatest disadvantage, the three-phase motor has the serious 
disadvantage that it runs at approximately constant speed at all loads. 
If a three-phase train encounters a grade, it does not ascend at reduced 
speed as do the other two types of motor, but it maintains its full 
speed throughout the ascent. This imposes severe peaks of load on 
the Electricity Supply Stations, whereas the reduced speed at which 
the other two types of motor automatically operate so soon as the 
grade is reached, protects the Electricity Supply Station from such 
wide variations in its load. The capital cost of an Electricity Supply 
Station for a given quantity of electricity delivered per annum is less 
the more uniform the load, A railway load is at the best far from 
uniform, and it is, consequently, the more important from this stand- 
point to avoid employing a type of motor with properties tending to 
accentuate the load-fluctuations on the Electricity Supply Station. 
A lesser disadvantage of the three-phase railway motor, but one 
which should, nevertheless, be mentioned, is the necessity for providing 
at least two supply conductors and at least two contact trolleys. 

The three-phase system has been very widely employed on the 
Italian State Eailways. Professor Kapp, in his Inaugural Presidential 
Address to the Institution of Electrical Engineers, on November 11, 
1909, quotes Mr. Verola, Chief Engineer of the Electrical Department 
of the Italian State Eailways, as follows : — 

"The decision to use the three-phase system is not final and 
absolute for our administration ; but the latter considers it preferable 
as a beginning, for the lines at present under electrification. The 
possibility to use the single-phase system in other cases which may 
better lend themselves to it, is thereby not excluded. In the case of 
three lines (Pontodecimo-Busalla, Bardonecchia Modane, and Savona- 
Ceva), which are about to be opened, the service is extremely heavy, 
trains of 400 tons and over having to be hauled up long grades of 
2*5 to 3*5 per cent, at a speed of 45 km ph. With the three-phase 
system it is possible to comply with these conditions by using two 
locomotives. These each weigh 60 tons, and each develop (at the 



1 88 ELECTRIC TRAINS 

1-hour rating) 2000 hp. They have five driving axles and two motors, 
which are placed above and between the three middle axles. Con- 
necting-rods transmit the motion from the motor to the driving axles. 
The three-phase system has the advantage that in running downhill 
the speed cannot exceed a certain limit, whilst recuperation of energy 
is possible. With the single-phase system, the weight of the motors 
would be at least doubled, resulting in a greater expenditure of energy, 
more especially as we shall be obliged always to use two locomotives 
to each train. The advantages of wider speed adjustment in running, 
and better efficiency in starting, are not of importance, since the grades 
are long and fairly uniform, and the distance between stations is great, 
whilst the latter are all on the level. For these reasons, and also on 
account of uniformity in the service, it is probable that also some 
future electrifications will be on the three-phase system, notably that 
of the prolongation of the Valtellina line to Milan, which will shortly 
be taken in hand. It is, however, highly probable that some other lines 
will be worked single-phase. One of these is the line Turin-Pinerolo- 
Torre-Pelice, where widely different speeds are necessary, the maximum 
being 80 km ph for 100-ton passenger trains." 

We now come to the second type, namely, the type of motor 
employing continuous electricity. The complete electrical train 
equipments employing this type of motor are, on the one hand, as 
light as equivalent three-phase equipments, and they are far lighter 
than equivalent single-phase equipments. 

Thus, a very conservative figure for the complete weight of electrical 
equipment when continuous motors are employed, is 19 kg per rated 
hp as against 40 kg per grated hp for the complete weight of the 
electrical equipment when single-phase motors are employed. 

Let us compare a typical continuous motor with a typical single- 
phase motor. Eor the former, we may take the G.E.69B already 
illustrated in Eig. 84, on p. 161, and for the latter, the W.E.51, of 
which an illustration is given in Fig. 88. For the commonly-accepted 
basis of rating of railway motors, namely 75° C. thermometrically- 
determined rise of temperature after one hour's run at constant load, 
the continuous motor has a capacity of 240 hp, as against a capacity 
of only 115 hp for the single-phase motor. The two motors have 
substantially the same over-all dimensions and weight, and yet the 
single-phase motor has only half the capacity of the continuous- 
electricity motor. 

It is not alone that single-phase motors are much larger and 
heavier for a given rated output, but also the remainder of the 
electrical equipment required on the single-phase system is very 
much more bulky and heavy than the corresponding apparatus for 
continuous equipments. 

As to the single-phase motor, efforts have been made to reduce its 



SUMMARY AND CONCLUSIONS 



189 



size by employing a blast of air provided by a ventilating set located 
at some suitable point on the truck, and from which air is forced to 




Fig. 88.— W.E.51 Single-phase Motor. 
One-hour Rating .... 115 hp. 
Weight (including Gearing) . . 2*75 tons. 
Speed at One-hour Rating . . 600 rpm. 

and through the motor. By these means, which are employed on the 
Siemens and the Westinghouse equipments on the single-phase trains 



I90 ELECTRIC TRAINS 

for the Heysham section of the Midland Railway, the motor weight 
has been brought down to 17'6 kg per hp as against 24 kg per hp for 
the weight of the single-phase motors on the S.L.E. line. On these 
S.L.E. motors, the only artificial ventilation is that provided by the 
small amount of air drawn through a hole in the armature shaft and 
subsequently escaping from the motor through openings in the case. 
Mr. Dawson, who has designed the electric trains on the S.L.E. Rail- 
way, considers this to be the best plan, notwithstanding the somewhat 
j^jreater weight of motor. On p. 165 of his book, entitled "Electric 
Traction on Railways," Mr. Dawson states — 

" Such methods (alluding to ventilation by means of fans), 
although used by most makers of single-phase motors, even in the 
case of motor cars, are not necessary, nor are they advisable, except 
where installed on electric locomotives, in the cabs of which plenty 
of room is available." 

The total weights of the electrical equipment on the S.L.E. 
trains have never (so far as I know) been made public. But assign- 
ing to the equipment additional to the motors the average of the 
weight per hp of the corresponding parts of the Siemens and the 
Westinghouse equipments on the Heysham section of the Midland 
Railway, we obtain for these additional equipments, a weight of 21 kg 
per rated hp capacity of the motor, which, added to the motor- weight 
of 24 kg per hp, gives 45 kg per hp as the complete weight of the 
electrical equipments on the S.L.E. trains, whereas for continuous- 
electricity equipments, the corresponding figure is almost always, in 
modern designs, well below 20 kg per rated hp of the motor. In 
Table LXI. I have brought together the leading data of the electrical 
and mechanical weights of some motor-coaches, which may be taken 
as typical of the practice of the last few years so far as regards both 
continuous and single-phase equipments. Certain striking con- 
clusions may be gleaned from this table. Thus, in the cases of the 11 
motor-coaches, fitted with continuous-electricity equipments, we find 
that the average ratio of the " total weight of the electrical equip- 
ment per motor-coach " to the " weight of all motors including 
gearing" is 1*30, the minimum and maximum values of the ratios 
being respectively 1'26 and 1*33. Thus there is great constancy 
in this ratio, and it may be taken as typical of continuous- electricity 
practice. Amongst the S.L.E. data, those marked with an asterisk 
are based on my own assumptions, since the data have not been 
published. It is not apparent how any progressive purpose can be 
served by withholding data of the weights of the equipments on this 
line. 

Numbers 12 to 15 of Table LXI. relate to motor-coaches fitted 
with single-phase equipments. From these data we see that the 
ratio of the weight of total electrical equipment to the weight of the 



SUMMARY AND CONCLUSIONS 



191 





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192 



ELECTRIC TRAINS 



motors is, for the average of the four equipments, 2*18. Thus it would 
appear that, for single-phase motor-coaches the weights of the motors 
must be doubled in order to arrive at the total weight of the electrical 
equipments. From Table LXI. we see that the weight of the 
S.L.E. 115-hp motor is 2*75 tons, or 24 kg per hp of rated capacity, 
as against 17*6 kg per rated hp and 18"8 kg per rated hp 
respectively for the two types of single-phase motors employed on 
the Heysham line, and 17*4 kg per rated hp for the Kotterdam- 
Hague Eailway. The average weight of these four single-phase 
motors is thus 19'5 kg per hp. Averaging the corresponding values 
for the eleven instances of continuous-electricity equipments, we 
obtain the value of 15 '6 kg per rated hp. The above figures, together 
with others of an interesting nature which have been deduced from 
Table LXI., are brought together in Table LXII. — 

Ta,ble LXII. — Average Values deduced from Data given in Table LXI. 





Motor-coach fitted 

with continuous 

equipments. 


Motor-coaches 
fitted with 
single-phase 
equipments. 


Percentage by 
which the weights 

of single-phase 
apparatus exceeds 

the weights of 
continuous equip- 
ments. 


Eatio of total weight of electrical 
equipment per motor-coach to 
weight of motors per motor-coach . 

Weight of motors with gear, in kg 
per hp 

Weight of total electrical equipment 
per motor-coach, in kg per hp 


1-30 
15-6 
20-2 


2-18 
19-5 
42-1 


25 
108 



While for the reasons already given, this great weight of electrical 
equipment tremendously handicaps the single-phase system as 
regards its application to suburban services, it does not constitute 
a disadvantage of such consequence, as compared with the continuous- 
electricity system, when dealing with long-distance runs with but 
few stops. But for long-distance runs with but few stops, it is 
not apparent that electrical methods of propulsion can yet show a 
net advantage over steam locomotive methods when all the various 
advantages and disadvantages are subjected to a careful comparison. 
It is, however, conclusively established that as a means of propulsion 
for suburban service, electrical methods show a great advantage over 
steam-locomotive methods. 

If, as is in my opinion probable, the suburban train mileage consti- 
tutes, on the railways of England, a very large or even a preponderating 
percentage of the total train mileage, then with the further advantages 



SUMMARY AND CONCLUSIONS 193 

of the greater cleanliness of electrical methods and the higher speeds, 
greater train weights and greater grade-ascending capacity which are all 
rendered practicable by electrical methods, it could ultimately become 
a sound proposition to also electrify the long-distance, non-stop 
sections. In that event, which, however, I regard as by no means 
imminent, the railways would be faced with the proposition of 
either using continuous electricity because it is the most suitable 
for the suburban sections, or else of using single-phase electricity 
because it is the most suitable for long-distance runs with but 
few stops, or else of using each in its appropriate place and changing 
over at the limits of a 2 5 -mile radius. The third proposition is in 
my opinion the correct one, the more especially since the suburban 
service is best handled by trains of motor-coaches, while the long- 
distance service is best handled by locomotives, and since, furthermore, 
the single-phase system is at a less disadvantage for locomotives. 
Trains despatched from a terminus and bound for a distant locality 
would be hauled to the boundary of the 25-mile radius by locomotives 
equipped with single-phase motors, which, as is well known, are oper- 
ative on circuits supplied with continuous electricity. After crossing 
the boundary of the 25-mile zone, these same locomotives would 
draw their supplies from the single-phase circuits with which the 
line would be equipped beyond the 25-mile zone. As a matter of 
experience, the continuous-electricity system of railway electrifica- 
tion has been demonstrated to meet, better than any other system, 
whether steam or electric, all the requirements of a high-speed, 
frequent-stop service where the trains are run at intervals of but a 
few minutes apart. For long-distance runs with infrequent trains, 
the single-phase system shows up to better advantage, but both 
are, in such a case, distinctly inferior to a steam -locomotive 
system. 

It mustnot be assumed that the series-wound, continuous-electricity 
motor has yet reached the limits of its development. On the contrary, 
there are various directions in which it may be still further perfected. 
Its weight may be slightly decreased by the device of forcing air 
through it, in a manner analogous to that often employed with 
single-phase motors, as, for instance, with the Siemens and the 
Westinghouse motors on the Heysham section of the Midland 
Eailway. By forced ventilation the rating of a motor may readily be 
increased by 25 per cent., and it is probable that still greater improve- 
ment in this direction will be found thoroughly practicable after a 
little more experience has been gained in this direction. It may 
certainly be considered as fully established that the weight of con- 
tinuous-electricity motors may be decreased by some 20 per cent, 
by means of employing forced ventilation, as is usually done with 
single-phase equipments. For schedules of only moderate severity 





194 



ELECTRIC TRAINS 



there is not sufficient occasion to resort to such methods for the 
continuous system, since the total weight of the electrical equipment 
is not then a large percentage of the total train weight. But the 
adoption of this method should be valuable for especially severe 
schedules where, even with continuous equipment, the total weight 
of the electrical equipment constitutes quite a large percentage of the 
total train weight. As showing the general order of magnitude of 
the percentage which the total weight of electrical equipment con- 
stitutes of the total train weight with continuous equipments, I 
have prepared Table LXIIT. — 

Table LXIII. 



Schedule speed 
(ml ph). 


Distance between 
stops (miles). 


Weight of electrical 
equipment as a per- 
centage of the total 
train weight. 


16 
25 
35 
43 


0-5 
1-0 
1-5 
2-0 


10 
20 
30 
40 



In corresponding schedules with single-phase equipments, these, 
where commercially possible, entail much greater weights of electrical 
equipment. Thus, on the South London Elevated Eailway, although 
the weight of the complete electrical equipment has not been 
published, it doubtless constitutes at least 41 tons out of the 138 tons 
of the total train weight, and is thus at least 29 per cent, of the total 
weight of the train, although the schedule speed is only 22 ml ph, 
with stops every 0'88 mile. 

Equipments comprising continuous-electricity motors are thus so 
reasonably light that it is legitimate to consider improving their 
quality even at the expense of slight increase in weight. It is with 
this thought that several companies are putting on the market 
continuous-electricity motors with interpoles. The Siemens-Schuckert 
Co. has supplied motors of this type for the Bonn-Cologne Eail- 
way which have the additional feature of being wound for 1000- 
volt continuous electricity. By means of this feature of interpoles, 
the obtaining of good commutation is so greatly simplified as to 
render the use of much higher pressures at the motor a thoroughly 
sound proposition. By substituting a pressure of 1200 volts for the 
now customary 600 volts, the sub-stations can be placed at least 
twice as far apart. This will further decrease the capital and operat- 
ing costs, and will give a much more uniform load on the sub-station, 



SUMMARY AND CONCLUSIONS 195 

since the load at any instant will be made up of the average of twice 
as many trains.* 

Manufacturers are at present making rapid progress toward the 
use of 1200 volts. Several inter-urban lines are at present either being 
installed or in operation, providing electricity to the coach or train at 
a pressure of at least 1200 volts. But in almost all instances, two 
600-volt motors insulated for 1200 volts are connected in series across 
the 1200 volts. In Table LXIV. is given a list of 11 roads where 
1200-volt continuous equipments are either being supplied or are 
already in operation. Amongst the above roads, Nos. VIII. and X. 
are of especial interest. These two roads were originally equipped 
with the single- phase system ; but the system proved unsatisfactory, 
and is being replaced by the high-pressure continuous-electricity 
equipments indicated in Table LXIV. The engineers of the Pennsyl- 
vania Eailway made some very thorough tests with a single-phase 
locomotive on a special testing track. The single-phase system was, 
however, found so distinctly inferior to the continuous system that 
the railway is obtaining 24 continuous-electricity locomotives to haul 
its trains through the tunnel approaches to New York City. Each of 
these 24 locomotives is of 4000-hp rated capacity, and is guaranteed to 
haul 500-ton trains at a speed of 70 ml ph. Each locomotive is of the 
articulated type, weighs 150 tons, and is equipped with two 2000-hp 
motors, the weight of each motor being 19 tons. These are the most 
powerful electric locomotives yet built. The Seebach-Wettingen line 
of the Swiss State Eailways was operated by the single-phase system 
for several years ; but the system was found to cost more than would 
be the case with steam-hauled trains, and the single-phase system is 
now being replaced by steam locomotives. 

These numerous set-backs are in striking contrast to the almost 
uniformly successful history of the continuous-electricity system of 
railway electrification. While the system as it stands is highly satis- 
factory, it may be of interest to mention certain other directions in 
which manufacturers are endeavouring to further develop it. Thus 
in a new line of railway motors with interpoles, advantage is taken 



* An interesting paper giving comparisons between 1200-volt and 600-volt 
continuous-electricity systems for various services has been read by C, E. Eveleth 
before the American Institute of Electrical Engineers (see «« Transactions," 1910, vol. 
xxix. pt. 1). 

The present author contributed an article to the Electrical Review (1904, vol. liv. 
pp. 693 and 765) entitled " The Continuous System and the Single-Phase System for 
Traction," in which comparisons were made between a 1300- volt continuous system 
with two standard motors in series, and a 3000-volt single-phase system. The article 
evoked correspondence {Electrical Review, vol. liv. p. 1031) which is also of interest as 
bearing so closely on a subject to which more attention is now being given. The 
method there advocated by the present author is that which is employed on the roads 
of which data is given in Table LXIV. 



196 



ELECTRIC TRAINS 



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SUMMARY AND CONCLUSIONS 197 

of the better commutation of such motors to introduce a more efficient 
method of control, namely, to regulate the field strength by varying 
resistance in parallel with the series winding. By adjusting the value 
of this resistance, the speed of the motor may be varied. It would 
appear probable that a distinct reduction in the energy required at the 
train should be effected by this method as compared with the ordinary 
speed-control method by means of resistance in series with the motor. 
Similar methods of control were often used many years ago on ordinary 
traction motors without interpoles, but were abandoned owing to the 
poor commutation performance of the motors when running with a 
shunted field. The reversion to this method of control, now that 
improved commutation by the use of interpoles is available, is a 
thoroughly rational proposition, and bids fair to be attended with 
success. 

Other interesting propositions relate to the employment of shunt- 
wound, continuous-electricity motors. Such motors can be made to 
act as generators by simply increasing the field strength above that 
corresponding to the speed at which the motor is running. This 
sends electricity back into the line. In other words, a large part of 
the momentum which, as we have seen, often constitutes a pre- 
ponderating percentage of the total energy sent into the train, may 
by this means be returned to the line instead of being wasted at the 
brake-shoes. A leading disadvantage is that since the motor serves 
not only to propel the car but also as a generator during braking, it 
is carrying current for nearly all the time, and consequently must be 
larger and heavier in order not to overheat. Consequently, the 
development of a rational regenerative control system should include 
the feature of forced ventilation of the motors. In addition to the 
very considerable saving in energy rendered practicable by regenera- 
tive control, there is a large saving due to the elimination of the 
wear between brake-shoes and wheels which, in ordinary equipments, 
entails heavy annual outlays for renewals. 



INDEX 



Acceleration, 2, 52, 108 et seq. 

conversion table for various units, 7, 8 

due to gravity, 118 

effect on comfort of passengers, 5 

„ electrical equipment on 

train, 5 
„ power station, 5 
,, stresses in rolling stock, 5 
graphical determination of, 110 
influence on energy consumption, 52, 
62-64 
,, speed-time diagram. 2-4 
instantaneous values of, 2, 111 
motor-characteristic, 9, 144 
of steam trains, 6, 184 
on Liverpool Overhead Railway, 5 
preferable values for, 6, 55 
rate of accelerating the, 5 
required to maintain various schedules, 

182 
straight-line, 2, 9 
Air-friction, 121 
Armstrong on train-friction, 128 
Arnold and Potter's tests on energy con- 
sumption, 128 
Aspinall on train-friction, 125, 129 
Average speed, 13 



B 



Baker Street and Waterloo Railway, 

receipts from passengers, 173 
Berlin-Zossen tests on train -friction, 121- 

122 
Blondel-Dubois formula for resistance on 

curves, 130 
Brakes, point of application of, 15 
Brake-shoes, losses at, 34, 40 
Braking portion of speed-time diagram, 11 



C 



C, VALUES of, in crest-speed formula, 48 
Capacity of equipment, 77,79, 113-114 



Carter, formula for inertia of rotating parts, 

30 
Central London Railway, 87 et seq. 

eflBciency of equipment, 91, 105 

gradients on, 87 

heating of motor on, 93, 158-160 

specification of train, 93-95 

tests of energy consumption od, 88-92 
Charing Cross, Euston and Hampstead 

Railway, receipts from passengers, 174 
Coasting, 11 

deceleration during, 11, 119 
Continuous-electricity motor, 

high-pressure, 194 

ventilation of, 159 

weight per hp, 188 
Costs of electrically equipped trains, 166 

et seq. 
Crest speed, 9 

formula for, 29 

momentum energy at, 29 
Curves, frictional resistance on, 129-130 

speed-time. See Speed-time Diagrams 
Cut-off, point of, 10 



D 



Dalziel and Sayer's tests. See Midland 

Railway 
Deceleration, 11, 52 

appropriate values for, 12 
during braking, 11 
,, coasting, 11, 119 
Diagram, speed-time. See Speed-time Dia- 
gram 
Dick-Kerr 150-hp motor, 84 
Distance-time curves, 
construction of, 18 
of electric train, 17 
of steam train, 17 
Drifting, 11 (see also Coasting) 
Dupuy, formula for frictional resistance on 

curves, 130 
Duration of stops, 19 et seq., 48 

on Loudon underground railways, 1, 
21 



199 



200 



INDEX 



E 
Efficiency 

of electrical equipment. See Electrical 

Equipment 
of G.E.66A motor, 90 
of G.E.69B motor, 102 
of propulsion, 36 
Electrical equipment, 

capacity of, 77, 79, 113-114 

costs of, 168 

effect of adding trailers on the efl&ciency 

of, 128 
efficiency of, 85, 67, 75 

„ ,, on Central London Rail- 
way, 91 
„ „ on Great Northern Picca- 
dilly and Brompton 
Railway, 101 
„ „ on Lancashire and York- 

shire Railway, 67 
„ „ on Midland Railway, 154 
losses in, 35, 67 

weight of, 93, 166 et seq., 190, 194 
Energy 

loss at brakes, 34, 40 
loss in electrical equipment, 35, 67 
of altitude, 88 
of momentum, 29 
train-friction, 33 
Energy-consumption. See also Tests of, 
Arnold and Potter's tests on, 128 
effect of adding trailers on, 128 
under ideal conditions, 44 et seq. 
Examples, 18, 26, 42, 66, 96, 114, 131 



F 

Forced ventilation of motors, 118, 188-190 
Formulae for 

crest speed, 29 

frictional resistance on curves, 130 

inertia of rotating parts, 30 

limiting schedule speed, 31 

momentum-energy at crest speed, 29 
Friction, 

air, 121 

gear, 119 

train. See Train-friction 
Frictional resistance. See Train-friction 



G 

G.E.66A Motor, 
efficiency, 90 
heating, 158-160 
weight, 95, 149 

G.E.69B motor, 
efficiency, 102 
heating, 160-162 



G.E.69B motor — continued, 

ventilation, 161 

weight, 103, 149 
Gear friction, 119 
„ loss, 158 
„ ratio, 133-134 
Gearless motors, efficiency of equipment, 75 
Gradients on Central London Railway, 87 
Graphical determination of 

acceleration, 110 

power curve, 112 
Gravity, momentum due to, 108 
Great Northern Piccadilly and Brompton 
Railway, 

efficiency of equipment, 101 

heating of motors, 160-162 

most economical schedule speed, 1 07 

receipts from passengers, 173 

specification of train, 102-104 

train-friction on, 101 

H 

Heating of motors, 74, 114, 158 et neq. 
Heysham single-phase line. See Midland 

Railway 
High-pressure continuous electricity system, 

194-196 
Hutchinson on frictional resistance of 

locomotives, 127 



Inertia of rotating parts, 29 
Carter's formula for, 30 



Lancashire and Yorkshire Railway, 

efficiency of equipment, 69 

heating of motors, 162-164 

specification of train, 84 

tests on, 67, 69 

train resistance on, 125-126 
Liverpool Overhead Railway, acceleration 

on, 5 
Locomotives, 

acceleration of steam, 6, 184 

frictional resistance of, 127 
Losses, 

brake-shoe, 34 

in controlling rheostats, 73 

in electrical equipment, 35, 

in motors, 158 et seq. 



67 



M 



Midland Railway, 145 et seq. 
gradients and curves on, 148 
specification of train, 150-152 
tests of trains, 147, 15 1 



INDEX 



201 



Momentum, 27 

due to gravity, 108 

of rotating parts, 29 

translational, 29, 108 
Motor characteristic, 

acceleration, 9 

of speed-time diagram, 9, 144 
Motor-coaches, particulars of weights, 190- 

192 
Motors, 

efficiency of, 72, 90, 102 

forced ventilation of, 118, 156 

heating of, 74, 114, 158 et seq. 

high -pressure, 194 

rating of, 74 

ventilation of, 118, 161, 188-190 

weights of, 159 (see also Specification 
of Trains) 
Moving-platform schemes, 23 



Pakallel arrangement of motors, 138, 139 

„ running, 73 

Power curve, 

calculation of, 132 et seq. 

graphical determination of, 112 
Propulsive efficiency, 36 



B 



Rating of railway motors, 74 
Rheostatic losses, 73 
Rolling stock, stresses imposed on, 5 
Rotational momentum, 29 
Rotterdam-Hague Railway, weights of 
motors, 192 



S 



Schedule speed, 13 

influence of distance between stops, 19 
et seq. 
„ stops per mile, 19 et seq. 

limits of, 51, 58 

on Great Northern Piccadilly and 
Brompton Railway, 107 
Series arrangement of motors, 138-139 

„ running, 73 
Service, severity of, 13, 23, 185 
Single-phase equipments, 
efficiency, 75 
rotational momentum, 29 
weight per hp, 190 
Single-phase motors, 

forced ventilation, 149, 188-190 
heating of, 152-153, 164 
weight per hp, 149, 188 



Smoke, elimination of, from tunnels, 181 
South London Elevated Rly., weight of 

equipment, 194 
Specification of trains. 

Central London Rly., 93-95 

G.N.P. and B..Rly., 102-104 

L. and Y. Rly., 84 

Midland Rly., 150-152 
Speed-time diagrams, 1 et seq. 

braking portion, 11-12 

coasting or drifting portion, 11 

constant-speed portion, 10 

motor-characteristic portion, 9-10, 144 

straight-line portion, 2, 9 
Straight-line acceleration, 2, 9 
Stresses imposed on rolling stock, 5 



Tests of energy consumption, 

C.L. Rly., 88 

L. and Y. Rly., 67,69 

G.N.P. and B. Rly., 100 

Arnold and Potter's, 128 
Three-phase system, 187 
Tractive-force. See Train- friction 
Train-friction, 31, 116 et seq. 

Armstrong on, 128 

Aspinall on, 125 

Berlin-Zossen tests, 121 

Effect of adding trailers on, 120, 124 
„ weight of train, 129 

Hutchinson on, 127 

on curves, 130 

on G.N.P. and B. Rly., 101 

on L. and Y. Rly., 125-126 
Train-tests. See Tests of Energy Con- 
sumption 
Translational momentum, 29, 108 



U 



Underground Electric Railways of 
London, 
duration of stop on, 21 



VENTijiATiON of motors, 
forced, 118, 188-190 
G.E.69B, 161 

W 

Weight 

of electrical equipment. See Electrical 

Equipment 
of motors. See Motors 



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Incandescent Stations, by C. J. Field; A Description of the Edison Electro- 
lyte Meter, by A. E. Kennelly; and a Paper on the Maximum Efficiency of 
Incandescent Lamps, by T. W, Howell. Fifth Edition. Illustrated. 
16mo., cloth, 140 pp. (No. 57 Van Nostrand's Science Series.). . . .50 cents 

INDUCTION COILS: How Made and How Used. Eleventh Edition. Illustrated. 
16mo., cloth, 123 pp. (No. 53 Van Nostrand's Science Series.). . .50 cents 



6 LIST OF WORKS ON ELECTRICAL SCIENCE. 

JEHL, FRANCIS, Member A.I.E.E. The Manufacture of Carbons for Electric 

Lighting and other purposes. Illustrated with numerous Diagrams, Tables, 
and Folding Plates. 8vo., cloth, 232 pp Net, $4.00 

JONES, HARRY C. The Electrical Nature of Matter and Radioactivity. 12mo., 
clcth, 212 pp $2.00 

KAPP, GISBERT. Electric Transmission of Energy and its Transformation, 
Subdivision, and Distribution. A Practical Handbook. Fourth Edition, 
thoroughly revised. Illustrated. 12mo., cloth, 445 pp $3.50 

Alternate-Current Machinery. Illustrated. 16mo., cloth, 190 pp. (No. 96 
Van Nostrand's Science Series.) 50 cents 

Dynamos, Alternators, and Transformers. Illustrated. 8vo., cloth, 507 
pp : $4.00 

KELSEY, W. R. Continuous-Current Dynamos and Motors, and their Control; 

being a series of articles reprinted from the ''Practical Engineer," and com- 
pleted by W R. Kelsey, B.Sc. With Tables, Figures, and Diagrams. 8vo., 
cloth, 439 pp $2.50 

KEMPE, H. R. A Handbook of Electrical Testing. Seventh Edition, 
revi&ed and enlarged. 285 Illustrations. 8vo.. cloth, 706 pp. . - .Net, $6.00 

KENNEDY, R. Modern Engines and Power Generators. Illustrated. 4to., 
cloth, 5 vols. Each $3 . 50 

Electrical Installations of Electric Light, Power, and Traction Machinery. 
Illustrated. Svo., cloth, 5 vols. Each $3 . 50 

KENNELLY, A. E. Theoretical Elements of Electro-Dynamic Machinery. Vol I. 
Illustrated. 8vo., cloth, 90 pp $1 . 50 

KERSHAW, J. B. C. The Electric Furnace in Iron and Steel Production. Illus- 
trated. 8vo., cloth, 74 pp Net, $1 .50 

Electrometallurgy. Illustrated. 8vo., cloth, 303 pp. (Van Nostrand's West- 
minster Series.) Net, $2 . 00 

KINZBRUNNER, C. Continuous-Current Armatures; their Winding and Con- 
struction. 79 Illustrations. 8vo., cloth, 80 pp Net, $1 .50 

Alternate-Current Windings; their Theory and Construction. 89 Illustrations. 
8vo., cloth, 80 pp Net, $1 . 50 

KOESTER, F. Steam-Electric Power Plants. A practical treatise on the design 
of central light and power stations and their economical construction and 
operation. Fully Illustrated. 4to., cloth, 455 pp Net, $5.00 

LARNER, E. T. The Principles of Alternating Currents for Students of Electrical 
Engineering. Illustrated with Diagrams. 12mo., cloth, 144 pp. Net, $1.50 

LEMSTROM, S. Electricity in Agriculture and Horticulture. Illustrated. 8vo., 
cloth Net, $1 .50 



LIST OF WORKS ON ELECTRICAL SCIENCE. 7 

LIVERMORE, V. P., and WILLIAMS, J. How to Become a Competent Motorman: 
Being a practical treatise on the proper method of operating a street-railway- 
motor-car; also giving details how to overcome certain defects. Second 
Edition. Illustrated. 16mo., cloth, 247 pp Net, $1 .00 

LOCKWOOD, T. D. Electricity, Magnetism, and Electro-Telegraphy. A Prac- 
tical Guide and Handbook of General Information for Electrical Students, 
Operators, and. Inspectors. Fourth Edition. Illustrated. 8vo., cloth, 
374 pp. . . $2.50 

LODGE, OLIVER J. Signalling Across Space Without Wires: Being a description 
of the work of Hertz and his successors. Third Edition. Illustrated. 8vo., 
cloth Net, $2 . 00 

LORING, A. E. A Handbook of the Electro-Magnetic Telegraph. Fourth Edition, 
revised. Illustrated. 16mo., cloth, 116 pp. (No. 39 Van Nostrand's 
Science Series.) 50 cents 

LUPTON, A. PARR, G. D. A., and PERKIN, H. Electricity Applied to Mining. 
Second Edition. With Tables, Diagrams, and Folding Plates. 8vo.. cloth 
320 pp Net, $4.50 

MAILLOUX, C. 0. Electric Traction Machinery. Illustrated. Svo., cloth. 

In Press 

MANSFIELD, A. K. Electromagnets: Their Design and Construction. Second 
Edition. Illustrated. IGmo., cloth, 155 pp. (Van Nostrand's Science 
Series No. 64.) 50 cents 

MASSIE, W. W., and UNDERHILL, C. R. Wireless Telegraphy and Telephony 
Popularly Explained. Illustrated. 12rao., cloth, 82 pp Net, $1 .00 

MAURICE, W. Electrical Blasting Apparatus and Explosives, with special refer- 
ence to colliery practice. Illustrated. 8vo., cloth, 167 pp Net, $3.50 

MAVSR, WM,, Jr. American Telegraphy and Encyclopedia of the Telegraph Sys- 
tems, Apparatus, Operations. Fifth Edition, revised. 450 Illustrations, 
8vo., cloth, 656 pp Net, $5.00 

MONCKTON, C. C. F. Radio Telegraphy. 173 Illustrations. 8vo., cloth, 272 pp. 
(Van Nostrand's Westminster Series.) Net, $2 .00 

MUNRO, J., and JAMIESON, A. A Pocket-Book of Electrical Rules and Tables 
for the Use of Electricians, Engineers, and Electrometallurgists. Eighteenth 
Revised Edition. 32mo., leather, 735 pp $2.50 

NIPHER, FRANCIS E. Theory of Magnetic Measurements. With an Appendix 
on the Method of Least Squares. Illustrated. 12mo., cloth, 94 pp. . .$1 .00 

NOLL, AUGUSTUS. How to Wire Buildings. A Manual of the Art of Interior 
Wiring. Fourth Edition. Illustrated. 12mo., cloth, 165 pp $1 .50 

OHM, G. S. The Galvanic Circuit Investigated Mathematically. Berlin, 1827. 
Translated by William Francis. With Preface and Notes by the Editor 
Thos. D. Lockwood. Second Edition. Illustrated. 16mo., cloth, 269 pp. 
(No. 102 Van Nostrand's Science Series.) • 50 cents 



8 LIST OF WORKS ON ELECTRICAL SCIENCE. 

OUDIN, MAURICE A. Standard Polyphase Apparatus and Systems. Illustrated 
with many Photo-reproductions, Diagrams, and Tables. Fifth Edition, revised. 
8vo., cloth, 369 pp Net, $3 .00 

PALAZ, A. Treatise on Industrial Photometry. Specially applied to Electric 
Lighting. Translated from the Frenqh by G. W, Patterson, Jr., Assistant 
Professor of Physics in the University of Michigan, and M. R. Patterson, 
B.A. Second Edition. Fully Illustrated. 8vo., cloth, 324 pp $4.00 

PARR, G. D. A. Electrical Engineering Measuring Instruments for Commercial 
and Laboratory Purposes. With 370 Diagrams and Engravings. 8vo., 
cloth, 328 pp Net, $3 . 50 

PARSHALL, H. F., and HOBART, H. M. Armature Windings of Electric Machines. 
Third Edition. With 140 full-page Plates, 65 Tables, and 165 pages of 

descriptive letter-press. 4to., cloth, 300 pp $7.50 

Electric Railway Engineering. With 437 Figures and Diagrams and many 
Tables. 4to., cloth, 475 pp. Net, $10.00 

Electric Machine Design. Being a revised and enlarged edition of " Electric 
Generators." 648 Illustrations. 4to, half morocco, 601 pp. . . .Net, $12.50 

PERRINE, F. A. C. Conductors for Electrical Distribution: Their Manufacture 
and Materials, the Calculation of Circuits, Pole-Line Construction, Under- 
ground Working, and other Uses. Second Edition. Illustrated. 8vo., 
cloth, 287 pp Net, $3.50 

POOLE, C. P. Wiring Handbook with complete Labor-saving Tables and Digest 
of Underwriters' Rules. Illustrated. 12mo., leather, 85 pp Net, $1 .00 

POPE, F. L. Modem Practice of the Electric Telegraph. A Handbook for Elec- 
tricians and Operators. Seventeenth Edition. Illustrated. 8vo., cloth, 
234 pp $1 .50 

RAPHAEL, F. C. Localization of Faults in Electric-Light Mains. Second Edition, 
revised. Illustrated. 8vo., cloth, 205 pp Net, $3 .00 

RAYMOND, E. B. Alternating-Current Engineering, Practically Treated. Third 
Edition, revised. With many Figures and Diagrams. 8vo., cloth, 244 pp.. 

Net, $2.50 

ROBERTS, J. Laboratory Work in Electrical Engineering — Preliminary Grade. 
A series of laboratory experiments for first- and second-year students in 
electrical engineering. Illustrated with many Diagrams. 8vo., cloth, 
218 pp Net, $2.00 

ROLLINS, W. Notes on X-Light. Printed on deckle edge Japan paper. 400 
pp. of text, 152 full-page plates. 8vo,, cloth Net, $7.50 

RUHMER, ERNST. Wireless Telephony in Theory and Practice. Translated 
from the German by James Erskine-Murray. Illustrated. 8vo., cloth, 
224 pp Net, $3 . 50 

RUSSELL, A. The Theory of Electric Cables and Networks. 71 Illustrations. 
Svo., cloth, 275 pp Net, $3 .00 



LIST OF WORKS ON ELECTRICAL SCIENCE. 9 

SALOMONS, DAVID. Electric-Light Installations. A Practical Handbook. Illus- 
trated. 12mo., cloth. 

Vol I.: Management of Acctimulators. Ninth Edition. 178 pp $2 .50 

Vol. II.: Apparatus. Seventh Edition. 318 pp $2 .25 

Vol. III.: Application. Seventh Edition. 234 pp $1 .50 

SCHELLEN, H. Magneto-Electric and Dynamo-Electric Machines. Their Con- 
struction and Practical Application to Electric Lighting and the Trans- 
mission of Power. Translated from the Third German Edition by N. S. 
Keith and Percy Neymann, Ph.D. With very large Additions and Notes 
relating to American Machines, by N. S. Keith. Vol. I. With 353 Illus- 
trations. Third Edition. 8vo., cloth, 518 pp $5 .00 

SEVER, G. F. Electrical Engineering Experiments and Tests on Direct-Current 
Machinery. Second Edition, enlarged. With Diagrams and Figures. 8vo., 
pamphlet, 75 pp Net, $1 .00 

and TOWNSEND, F. Laboratory and Factory Tests in Electrical Engineering. 

Second Edition. Illustrated. 8vo., cloth, 269 pp Net, $2 . 50 

SEWALL, C. H. Wireless Telegraphy. With Diagrams and Figures. Second 

Edition, corrected. Illustrated, 8vo., cloth, 229 pp Net, $2.00 

Lessons in Telegraphy. Illustrated. 12mo., cloth, 104 pp Net, $1 .00 

T. Elements of Electrical Engineering. Third Edition, revised. Illustrated. 

8vo., cloth, 444 pp $3.00 

The Construction of Dynamos (Alternating and Direct Current). A Text- 
book for students, engineering contractors, and electricians-in-charge. 
Illustrated. 8vo., cloth, 316 pp $3.00 

SHAW, P. E. A First- Year Course of Practical Magnetism and Electricity. Spe- 
cially adapted to the wants of technical students. Illustrated. 8vo., 
cloth, 66 pp. interleaved for note taking Net, $1 .00 

SHELDON, S., and MASON, H. Dynamo-Electric Machinery: Its Construction, 
Design, and Operation. 
Vol. I.: Direct-Current Machines. Seventh Edition, revised. Illustrated. 
8vo., cloth, 281 pp Net, $2.50 

and HAUSMANN, E. Alternating-Current Machines : Being the second volume 

of " Dynamo -Electric Machinery; its Construction, Design, and Opera- 
tion." With many Diagrams and Figures. (Binding uniform with Vol- 
ume I.) Seventh Edition, rewritten. 8vo., cloth, 353 pp Net, $2 . 50 

SLOANE, T. O'CONOR. Standard Electrical Dictionary. 300 Illustrations. 12mo., 
cloth, 682 pp .$3 .00 

Elementary Electrical Calculations. How Made and Applied. Illustrated. 
8vo., cloth, 300 pp In Press 

SNELL, ALBION T. Electric Motive Power. The Transmission and Distribution 
of Electric Power by Continuous and Alternating Currents. With a Section 
on the Applications of Electricity to Mining Work. Second Edition. 
Illustrated. 8vo., cloth, 411 pp Net, $4.00 



10 LIST OF WORKS ON ELECTRICAL SCIENCE. 

SODDY, F. Radio-Activity ; an Elementary Treatise from the Standpoint of the 
Disintegration Theory. Fully Illustrated. 8vo., cloth, 214 pp. .Net, $3.00 

SOLOMON, MAURICE. Electric Lamps. Illustrated. 8vo., cloth. (Van Nos- 
trand's Westminster Series.) Net, $2 .00 

STEWART, A. Modern Polyphase Machinery. Illustrated. 12mo., cloth, 296 
pp Net, $2 . 00 

SWINBURNE, JAS., and WORDINGHAM, C. H. The Measurement of Electric 
Currents. Electrical Measuring Instruments. Meters for Electrical Energy. 
Edited, with Preface, byT. Commerford Martin. Folding Plate and Numer- 
ous Illustrations. 16mo., cloth, 241 pp. (No. 109 Van Nostrand's Science 
Series.) 50 cents 

SWOOPE, C. WALTON. Lessons in Practical Electricity: Principles, Experi- 
ments, and Arithmetical Problems. An Elementary Text-book. With 
numerous Tables, Formulae, and two large Instruction Plates. Ninth 
Edition. Illustrated. 8vo., cloth, 462 pp Net, $2 .00 

THOM, C, and JONES, W. H. Telegraphic Connections, embracing recent methods 
in Quadruplex Telegraphy. 20 Colored Plates. Svo., cloth, 59 pp. $1.50 

THOMPSON, S. P., Prof. Dynamo-Electric Machinery. With an Introduction 
and Notes by Frank L. Pope and H. R. Butler. Fully Illustrated. lOmo., 
cloth, 214 pp, (No. 66 Van Nostrand's Science Series.) 50 cents 

Recent Progress in Dynamo-Electric Machines. Being a Supplement to 
"Dynamo-Electric Machinery." Illustrated. 16mo., cloth, 113 pp. (No. 
75 Van Nostrand's Science Series.) 50 cents 

TOWNSEND, FITZHUGH. Alternating Current Engineering. Illustrated. 8vo., 
paper, 32 pp Net, 75 cents 

UNDERBILL, C. R. The Electromagnet: Being a new and revised edition of 
"The Electromagnet," by Townsend Walcott, A. E. Kennelly, and Richard 
Varley. With Tables and Numerous Figures and Diagrams. 12mo., 
cloth New Revised Edition in Press 

URQUHART, J. W. Dynamo Construction. A Practical Handbook for the use 
of Engineer Constructors and Electricians in Charge. Illustrated. 12mo., 
cloth $3.00 

Electric Ship-Lighting. A Handbook on the Practical Fitting and Running of 
Ship's Electrical Plant, for the use of Ship Owners and Builders, Marine 
Electricians, and Sea-going Engineers in Charge. 88 Illustrations. 12mo., 
cloth, 308 pp $3.00 

Electric-Light Fitting. A Handbook for Working Electrical Engineers, em- 
bodying Practical Notes on Installation Management. Second Edition. 
With numerous Illustrations. 12mo., cloth $2 .00 

Electroplating. Fifth Edition. Illustrated. 12mo., cloth, 230 pp $2.00 

Electrotyping. Illustrated. 12mo., cloth, 228 pp '. $2.00 



LIST OF WORKS ON ELECTRICAL SCIENCE. 11 

WADE, E. J. Secondary Batteries: Their Theory, Construction, and Use. With 
innumerable Diagrams and Figures. 8vo., doth New Edition in Press 

WALKER, FREDERICK. Practical Dynamo-Building for Amateurs. How to 
Wind for any Output. Third Edition. Illustrated. 16mo., cloth, 104 pp. 
(No. 98 Van Nostrand's Science Series.) 50 cents 

SYDNEY F. Electricity in Homes and Workshops. A Practical Treatise on 

Auxiliary Electrical Apparatus. Fourth Edition. Illustrated. 12mo., 
cloth, 358 pp $2 .00 

Electricity in Mining. Illustrated. 8vo., cloth, 385 pp $3.50 

WALLING, B. T., Lieut.-Com. U.S.N., and MARTIN, JULIUS. Electrical Installa- 
tions of the United States Navy. With many Diagrams and Engravings. 
8vo., cloth, 648 pp $6.00 

WALMSLEY, R. M. Electricity in the Service of Man. A Popular and Practical 
Treatise on the Application of Electricity in Modern Life. Illustrated. 
8vo., cloth, 1208 pp Net, $4.50 

WATT, ALEXANDER. Electroplating and Refining of Metals. New Edition, 

rewritten by Arnold Philip. Illustrated. 8vo., cloth, 677 pp. .Net, $4.50 

Electro-Metallurgy. Fifteenth Edition. Illustrated. 12mo., cloth, 225 pp., 

$1.00 

WEBB, H. ,L. A Practical Guide to the Testing of Insulated Wires and Cables. 
Fifth Edition. Illustrated. 12mo., cloth, 118 pp $1 .00 

WEEKS, R. W. The Design of Alternate-Current Transformer. New Edition 

in Press 

WEYMOUTH, F. MARTEN. Drum Armatures and Commutators. (Theory and 
Practice.) A complete treatise on the theory and construction of drum- 
winding, and of commutators for closed-coil armatures, together with a full 
resume of some of the principal points involved in their design, and an 
exposition of armature reactions and sparking. Illustrated. 8vo., cloth, 
295 pp Net, $3.00 

WILKINSON, H. D. Submarine Cable-Laying, Repairing, and Testing. New Edition. 
Illustrated. 8vo., cloth.. In Press 

YOUNG, J. ELTON. Electrical Testing for Telegraph Engineers. Illustrated. 
8vo., cloth, 264 pp Net, $4.00 

A 112=page Catalog of Books on Electricity, classified by 
subjects, will be furnished gratis, postage prepaid, on 
application. 



THE NEW FOSTER l 

Fifth Edition, Completely Revised and 
Enlarged, with Four-fifths of Old Matter 
Replaced by New, Up-to-date Material. 
Pocket size, flexible leather, elaborately 
illustrated, with an extensive index, 1636 
pp., Thumb Index, etc. Price, $5.00. 

ELECTRICAL 

ENGINEER'S 

POCKETBOOK 

The Most Complete Book of Its Kind Ever Published, 

Treating of the Latest and Best Practice 
in Electrical Engineering 

By HORATIO A. FOSTER 

Member Am. Inst. E. E., Member Am. Soc. M. E. 




With the Collaboration of Eminent Specialists 



Symbols, Units, Instruments 

Measurements 

/lagnetic Properties of Iron 

llectro-Magnets 

Properties of Conductors 

delations and Dimensions of 
Conductors 

Jnderground Conduit Con- 
struction 

tandard Symbols 

!able Testing 

)ynamos and Motors 

ests of Dynamos and Motors 



CONTENTS 

The Static Transformer 
Standardization Rules 
Illuminating Engineering 
Electric Lighting (Arc) 

(Incandescent) 
Electric Street Railways 
Electrolysis 

Transmission of Power 
Storage Batteries 
Switchboards 
Lightning Arresters 
Electricity Meters 
Wireless Telegraphy 
Telegraphy 



Telephony 

Electricity in the U. S. Army 

Electricity in the U. S. Navy 

Resonance 

Electric Automobiles 

Electro-chemistry and Electro- 
metallurgy 

X-Rays 

Electric Heating, Cooking and 
Welding 

Lightning Conductors 

Mechanical Section 

Index 



D. VAN NOSTRAND COflPANY, 

Publishers and Booksellers, 

23 MURRAY AND 27 WARREN STREETS, NEW YORK. 



